{"id":35381,"date":"2025-01-01T13:00:30","date_gmt":"2025-01-01T13:00:30","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=35381"},"modified":"2025-12-14T23:31:16","modified_gmt":"2025-12-14T23:31:16","slug":"%d0%bc%d0%b0%d0%ba%d1%81%d0%b8%d0%bc%d1%83%d0%bc%d1%8b-%d0%b8-%d0%bc%d0%b8%d0%bd%d0%b8%d0%bc%d1%83%d0%bc%d1%8b-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ru\/%d0%bc%d0%b0%d0%ba%d1%81%d0%b8%d0%bc%d1%83%d0%bc%d1%8b-%d0%b8-%d0%bc%d0%b8%d0%bd%d0%b8%d0%bc%d1%83%d0%bc%d1%8b-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8\/","title":{"rendered":"\u041c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u044b \u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438"},"content":{"rendered":"<style>\np, ul, ol{\ntext-align: justify;\n}\nh1{\ntext-align:center;\ntext-transform: uppercase;\n}\nh2{\ntext-align:center;\ntext-transform: uppercase;\nfont-size:24pt;\n}\nh3 { \n    text-align: center;\n    text-transform: uppercase;\n    font-size: 24px !important;\n}\n<\/style>\n<h1>\u041c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u044b \u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/h1>\n<p style=\"text-align:center\"><em>\u0413\u0434\u0435 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u00ab\u043d\u0430\u0438\u043b\u0443\u0447\u0448\u0430\u044f\u00bb \u0442\u043e\u0447\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438: \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c, \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u0432\u044b \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0435\u0441\u044c \u0434\u043e\u0441\u0442\u0438\u0447\u044c, \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c, \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0438\u0437\u0431\u0435\u0436\u0430\u0442\u044c? \u042d\u0442\u043e\u0442 \u0432\u043e\u043f\u0440\u043e\u0441, \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u044e\u0449\u0438\u0439 \u0432 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438, \u0444\u0438\u0437\u0438\u043a\u0435, \u044d\u043a\u043e\u043d\u043e\u043c\u0438\u043a\u0435 \u0438 \u0438\u043d\u0436\u0435\u043d\u0435\u0440\u0438\u0438, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0434\u043d\u0438\u043c \u0438\u0437 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0445 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0439 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0438\u0441\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f. \u0418 \u0432\u043e\u0442 \u043a\u043b\u044e\u0447\u0435\u0432\u043e\u0439 \u043c\u043e\u043c\u0435\u043d\u0442: <a href=\"https:\/\/toposuranos.com\/material\/ru\/%d1%82%d0%b5%d0%be%d1%80%d0%b5%d0%bc%d0%b0-%d0%b2%d0%b5%d0%b9%d0%b5%d1%80%d1%88%d1%82%d1%80%d0%b0%d1%81%d1%81%d0%b0-%d0%be-%d0%bd%d0%b0%d0%b8%d0%b1%d0%be%d0%bb%d1%8c%d1%88%d0%b8%d1%85-%d0%b8-%d0%bd\/\" rel=\"noopener\" target=\"_blank\">\u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u0412\u0435\u0439\u0435\u0440\u0448\u0442\u0440\u0430\u0441\u0441\u0430<\/a> \u0433\u0430\u0440\u0430\u043d\u0442\u0438\u0440\u0443\u0435\u0442, \u0447\u0442\u043e \u0435\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u0438 \u0432\u044b \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442\u0435 \u043d\u0430 \u0437\u0430\u043c\u043a\u043d\u0443\u0442\u043e\u043c \u0438 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435, \u0442\u043e <strong>\u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u044b\u0435 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u044b \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442<\/strong>. \u0421 \u044d\u0442\u043e\u0433\u043e \u043c\u043e\u043c\u0435\u043d\u0442\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439: \u043d\u0430\u0443\u0447\u0438\u0442\u044c\u0441\u044f \u0432\u044b\u044f\u0432\u043b\u044f\u0442\u044c <strong>\u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u044b<\/strong> \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e <strong>\u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0442\u043e\u0447\u0435\u043a<\/strong> (<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f&#039;(x)=0<\/span><\/span> \u0438\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442) \u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0442\u0430\u043a\u0438\u0435 \u0438\u043d\u0441\u0442\u0440\u0443\u043c\u0435\u043d\u0442\u044b, \u043a\u0430\u043a \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u0420\u043e\u043b\u043b\u044f \u0438 \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u043e \u0441\u0440\u0435\u0434\u043d\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0438, \u0447\u0442\u043e\u0431\u044b \u043f\u0440\u0435\u0432\u0440\u0430\u0442\u0438\u0442\u044c \u00ab\u0441\u043b\u0435\u043f\u043e\u0439\u00bb \u043f\u043e\u0438\u0441\u043a \u0432 \u0447\u0435\u0442\u043a\u0438\u0439, \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u0435\u043c\u044b\u0439 \u0438 \u044d\u0444\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u044b\u0439 \u043c\u0435\u0442\u043e\u0434.<\/em><\/p>\n<p style=\"text-align:center\">\n<strong>\u0426\u0435\u043b\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f:<\/strong>\n<\/p>\n<ol>\n<li><b>\u0412\u044b\u043f\u043e\u043b\u043d\u044f\u0442\u044c<\/b> \u043f\u043e\u043b\u043d\u044b\u0439 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u044b\u0445 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u043e\u0432 \u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span>: \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0432 \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u0438\u0445 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0442\u043e\u0447\u043a\u0430\u0445 \u0438 \u043d\u0430 \u043a\u043e\u043d\u0446\u0430\u0445 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0430, \u0430 \u0437\u0430\u0442\u0435\u043c \u0441\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0442\u044c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0433\u043e \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u0430 \u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u0430.\n  <\/li>\n<li><strong>\u0421\u043e\u043f\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0442\u044c<\/strong> \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0433\u043e \u0438 \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e\u0433\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u044f: \u043f\u043e\u043d\u0438\u043c\u0430\u0442\u044c, \u0447\u0442\u043e \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u00ab<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f&#039;(x_0)=0<\/span><\/span>\u00bb \u043d\u0435 \u0433\u0430\u0440\u0430\u043d\u0442\u0438\u0440\u0443\u0435\u0442 \u043d\u0430\u043b\u0438\u0447\u0438\u0435 \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430, \u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0442\u044c, \u043a\u0430\u043a\u0438\u0435 \u0434\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u0430 (\u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439, \u0430\u043d\u0430\u043b\u0438\u0437 \u0437\u043d\u0430\u043a\u043e\u0432, \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435) \u0443\u043c\u0435\u0441\u0442\u043d\u044b \u0432 \u043a\u0430\u0436\u0434\u043e\u043c \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435.\n  <\/li>\n<li><strong>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0442\u044c<\/strong> \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u044d\u0444\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u0443\u044e \u0441\u0442\u0440\u0430\u0442\u0435\u0433\u0438\u044e \u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043e\u0442 \u0442\u0438\u043f\u0430 \u0437\u0430\u0434\u0430\u0447\u0438: \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u044b\u0435 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u044b \u043d\u0430 \u043a\u043e\u043c\u043f\u0430\u043a\u0442\u043d\u044b\u0445 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0430\u0445 (\u0412\u0435\u0439\u0435\u0440\u0448\u0442\u0440\u0430\u0441\u0441 + \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0439) \u0432 \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u0441 \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430\u043c\u0438 \u0432\u043e \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u0438\u0445 \u0442\u043e\u0447\u043a\u0430\u0445 (\u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 + \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0439 \u0430\u043d\u0430\u043b\u0438\u0437), \u0441 \u043e\u0431\u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0441\u0434\u0435\u043b\u0430\u043d\u043d\u043e\u0433\u043e \u0432\u044b\u0431\u043e\u0440\u0430.\n  <\/li>\n<\/ol>\n<p style=\"text-align:center;\">\n<strong><u>\u0421\u041e\u0414\u0415\u0420\u0416\u0410\u041d\u0418\u0415<\/u>:<\/strong><br \/>\n<a href=\"#1\"><strong>\u041c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u044b \u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u044b, \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u044b\u0435 \u0438 \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u044b<\/strong><\/a><br \/>\n<a href=\"#2\">\u041a\u0440\u0438\u0442\u0435\u0440\u0438\u0439 \u043f\u0435\u0440\u0432\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439<\/a><br \/>\n<a href=\"#3\"><strong>\u0422\u0435\u043e\u0440\u0435\u043c\u0430 \u0420\u043e\u043b\u043b\u044f<\/strong><\/a><br \/>\n<a href=\"#4\"><strong>\u0414\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u043e \u0441\u0440\u0435\u0434\u043d\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0438<\/strong><\/a><br \/>\n<a href=\"#5\">\u0418\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044f \u0438 \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044f<\/a>\n<\/p>\n<div style=\"text-align: center;\">\n  <iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/OscTlX3raaE\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<\/div>\n<p style=\"text-align: justify;\">\n  <a href=\"https:\/\/toposuranos.com\/material\/ru\/%d1%82%d0%b5%d0%be%d1%80%d0%b5%d0%bc%d0%b0-%d0%b2%d0%b5%d0%b9%d0%b5%d1%80%d1%88%d1%82%d1%80%d0%b0%d1%81%d1%81%d0%b0-%d0%be-%d0%bd%d0%b0%d0%b8%d0%b1%d0%be%d0%bb%d1%8c%d1%88%d0%b8%d1%85-%d0%b8-%d0%bd\/\" rel=\"noopener\" target=\"_blank\">\u0422\u0435\u043e\u0440\u0435\u043c\u0430 \u0412\u0435\u0439\u0435\u0440\u0448\u0442\u0440\u0430\u0441\u0441\u0430<\/a> \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0430\u0435\u0442, \u0447\u0442\u043e \u0435\u0441\u043b\u0438 \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430 \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u043d\u0430 \u0437\u0430\u043c\u043a\u043d\u0443\u0442\u043e\u043c \u0438 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u043e\u043c \u043f\u043e\u0434\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span>, \u0442\u043e \u043e\u043d\u0430 \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442 \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0438 \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 (\u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u044b\u0445 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u043e\u0432). \u041f\u043e\u0438\u0441\u043a \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u0432 \u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <strong>\u0437\u0430\u0434\u0430\u0447\u0435\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438<\/strong>, \u0438 \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u0412\u0435\u0439\u0435\u0440\u0448\u0442\u0440\u0430\u0441\u0441\u0430 \u0433\u0430\u0440\u0430\u043d\u0442\u0438\u0440\u0443\u0435\u0442 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043e\u0432\u0430\u043d\u0438\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0439 \u0432 \u0441\u043c\u044b\u0441\u043b\u0435 \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u044b\u0445 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u043e\u0432 \u043f\u0440\u0438 \u0443\u0441\u043b\u043e\u0432\u0438\u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043a\u043e\u043c\u043f\u0430\u043a\u0442\u043d\u043e\u0441\u0442\u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f. \u041f\u043e\u0441\u043b\u0435 \u0442\u043e\u0433\u043e \u043a\u0430\u043a \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043e\u0432\u0430\u043d\u0438\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0439 \u043e\u0431\u0435\u0441\u043f\u0435\u0447\u0435\u043d\u043e, \u043e\u0441\u0442\u0430\u0435\u0442\u0441\u044f \u043b\u0438\u0448\u044c \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0430\u0442\u044c \u0441\u0442\u0440\u0430\u0442\u0435\u0433\u0438\u0438, \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0449\u0438\u0435 \u044d\u0442\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0430\u0439\u0442\u0438.\n<\/p>\n<p><a name=\"1\"><\/a><\/br><\/p>\n<h2>\u041c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u044b \u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u044b, \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u044b\u0435 \u0438 \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u044b<\/h2>\n<p style=\"text-align: justify;\">\n  <a href=\"https:\/\/www.youtube.com\/watch?v=OscTlX3raaE&amp;t=156s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">\u041f\u0440\u0435\u0436\u0434\u0435 \u0447\u0435\u043c \u043f\u0440\u0438\u0441\u0442\u0443\u043f\u0438\u0442\u044c \u043a \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043d\u0438\u044e<\/span><\/a> \u0441\u0442\u0440\u0430\u0442\u0435\u0433\u0438\u0439 \u043f\u043e\u0438\u0441\u043a\u0430 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u0432 \u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432, \u0447\u0435\u0442\u043a\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u043c, \u0447\u0442\u043e \u0438\u043c\u0435\u043d\u043d\u043e \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u043d\u0430\u0439\u0442\u0438.<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #e0ffe0;\">\n<p style=\"text-align: justify;\">\n          <span style=\"color: #000080;\"><strong>\u041e\u041f\u0420\u0415\u0414\u0415\u041b\u0415\u041d\u0418\u0415:<\/strong><\/span><br \/>\n\u041f\u0443\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0441 \u043e\u0431\u043b\u0430\u0441\u0442\u044c\u044e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D<\/span><\/span>. \u0411\u0443\u0434\u0435\u043c \u0433\u043e\u0432\u043e\u0440\u0438\u0442\u044c, \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442 <strong>\u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0433\u043e \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u0430<\/strong> \u0432 \u0442\u043e\u0447\u043a\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in D<\/span><\/span>, \u0435\u0441\u043b\u0438:\n        <\/p>\n<p style=\"text-align: center;\">\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left( \\forall x \\in D \\right)\\bigl(f(x) \\leq f(x_0)\\bigr)<\/span><\/span>\n        <\/p>\n<p style=\"text-align: justify;\">\n          \u0438 \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442 <strong>\u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0433\u043e \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u0430<\/strong> \u0432 \u0442\u043e\u0447\u043a\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span>, \u0435\u0441\u043b\u0438:\n        <\/p>\n<p style=\"text-align: center;\">\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left( \\forall x \\in D \\right)\\bigl( f(x_0) \\leq f(x)\\bigr)<\/span><\/span>\n        <\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\n  \u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0442\u0441\u044f \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u044b (\u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f).\n<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #e0ffe0;\">\n<p style=\"text-align: justify;\">\n          <span style=\"color: #000080;\"><strong>\u041e\u041f\u0420\u0415\u0414\u0415\u041b\u0415\u041d\u0418\u0415:<\/strong><\/span><br \/>\n          \u041f\u0443\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0441 \u043e\u0431\u043b\u0430\u0441\u0442\u044c\u044e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D<\/span><\/span>, \u0438 \u043f\u0443\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in D<\/span><\/span>. \u0411\u0443\u0434\u0435\u043c \u0433\u043e\u0432\u043e\u0440\u0438\u0442\u044c, \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442 <strong>\u043b\u043e\u043a\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u0430<\/strong> \u0432 \u0442\u043e\u0447\u043a\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span>, \u0435\u0441\u043b\u0438:\n        <\/p>\n<p style=\"text-align: center;\">\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\exists h&gt;0)\\left( \\forall x\\in [x_0-h, x_0+h] \\cap D \\right)\\bigl(f(x) \\leq f(x_0)\\bigr)<\/span><\/span>\n        <\/p>\n<p style=\"text-align: justify;\">\n          \u0438 \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442 <strong>\u043b\u043e\u043a\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u0430<\/strong> \u0432 \u0442\u043e\u0447\u043a\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span>, \u0435\u0441\u043b\u0438:\n        <\/p>\n<p style=\"text-align: center;\">\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\exists h&gt;0)\\left( \\forall x\\in [x_0-h, x_0+h] \\cap D \\right)\\bigl( f(x_0) \\leq f(x)\\bigr)<\/span><\/span>\n        <\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\n  \u0418\u0441\u0445\u043e\u0434\u044f \u0438\u0437 \u044d\u0442\u043e\u0433\u043e, \u043c\u043e\u0436\u043d\u043e \u0441\u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442:\n<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #ffe0e0;\">\n<p style=\"text-align: justify;\">\n          <span style=\"color: #800000;\"><strong>\u0422\u0415\u041e\u0420\u0415\u041c\u0410:<\/strong><\/span><br \/>\n          <a href=\"https:\/\/www.youtube.com\/watch?v=OscTlX3raaE&amp;t=833s\" target=\"_blank\" rel=\"noopener\"><br \/>\n            <strong><span style=\"color: #ff0000;\">\u041f\u0443\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u2014 \u0442\u043e\u0447\u043a\u0430<\/span><\/strong><\/a> \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u044f\u044f \u0442\u043e\u0447\u043a\u0430 \u043a\u043e\u043c\u043f\u0430\u043a\u0442\u043d\u043e\u0433\u043e \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/span>. \u0415\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442 <strong>\u043b\u043e\u043a\u0430\u043b\u044c\u043d\u043e\u0433\u043e<\/strong> \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u0430 \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u0430 \u0432 \u0442\u043e\u0447\u043a\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x_0)<\/span><\/span> \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442, \u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x_0)=0<\/span><\/span>.\n        <\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #e0e0ff;\">\n<p style=\"text-align: justify;\">\n          <span style=\"color: #000080;\"><strong>\u0414\u041e\u041a\u0410\u0417\u0410\u0422\u0415\u041b\u042c\u0421\u0422\u0412\u041e:<\/strong><\/span><br \/>\n          \u041f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043c, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442 \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u0430 \u0432 \u0442\u043e\u0447\u043a\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span>. \u0422\u043e\u0433\u0434\u0430 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h_0 \\gt 0<\/span><\/span> \u0442\u0430\u043a\u043e\u0435, \u0447\u0442\u043e \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0433\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h<\/span><\/span>, \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u044e\u0449\u0435\u0433\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u044e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|h|\\lt h_0<\/span><\/span> \u0438 \u043f\u0440\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0+h\\in I<\/span><\/span>, \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f:\n        <\/p>\n<p style=\"text-align: center;\">\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x_0 + h)\\leq f(x_0)<\/span><\/span>\n        <\/p>\n<p style=\"text-align: justify;\">\n          \u0447\u0442\u043e \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e:\n        <\/p>\n<p style=\"text-align: center;\">\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x_0 + h) - f(x_0)\\leq 0<\/span><\/span>\n        <\/p>\n<p style=\"text-align: justify;\">\n          \u0422\u0435\u043f\u0435\u0440\u044c \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0434\u0432\u0430 \u0441\u043b\u0443\u0447\u0430\u044f:\n        <\/p>\n<ul>\n<li>\n<p style=\"text-align: justify;\">\n              \u0415\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h&gt;0<\/span><\/span>, \u0442\u043e:\n            <\/p>\n<p style=\"text-align: center;\">\n              <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{f(x_0 + h) - f(x_0)}{h}\\leq 0<\/span><\/span>\n            <\/p>\n<\/li>\n<li>\n<p style=\"text-align: justify;\">\n              \u0415\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h\\lt 0<\/span><\/span>, \u0442\u043e:\n            <\/p>\n<p style=\"text-align: center;\">\n              <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{f(x_0 + h) - f(x_0)}{h}\\geq 0<\/span><\/span>\n            <\/p>\n<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\n          \u0415\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x_0)<\/span><\/span> \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442, \u0442\u043e \u043f\u0440\u0435\u0434\u0435\u043b \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u043d\u043e\u0433\u043e \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044f \u043f\u0440\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h\\to 0<\/span><\/span> \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0438 \u0434\u043e\u043b\u0436\u0435\u043d \u0431\u044b\u0442\u044c \u0441\u043e\u0433\u043b\u0430\u0441\u043e\u0432\u0430\u043d \u0441 \u043e\u0431\u0435\u0438\u043c\u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430\u043c\u0438, \u0447\u0442\u043e \u0432\u044b\u043d\u0443\u0436\u0434\u0430\u0435\u0442:\n        <\/p>\n<p style=\"text-align: center;\">\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle f^\\prime(x_0)=\\lim_{h\\to 0}\\frac{f(x_0 + h) - f(x_0)}{h}= 0<\/span><\/span>\n        <\/p>\n<p style=\"text-align: justify;\">\n          \u0427\u0442\u043e \u0438 \u0442\u0440\u0435\u0431\u043e\u0432\u0430\u043b\u043e\u0441\u044c \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u044c.\n        <\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\n  \u0421\u043b\u0435\u0434\u0443\u0435\u0442 \u043e\u0442\u043c\u0435\u0442\u0438\u0442\u044c, \u0447\u0442\u043e \u0434\u0430\u043d\u043d\u043e\u0435 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u043e \u0442\u0430\u043a\u0436\u0435 \u0441\u043f\u0440\u0430\u0432\u0435\u0434\u043b\u0438\u0432\u043e \u0434\u043b\u044f \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432. \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0440\u0430\u0441\u0441\u0443\u0436\u0434\u0435\u043d\u0438\u0435 \u043d\u0430\u0447\u0438\u043d\u0430\u0435\u0442\u0441\u044f \u0441 \u0443\u0441\u043b\u043e\u0432\u0438\u044f: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x_0+h)\\ge f(x_0)<\/span><\/span> \u0434\u043b\u044f \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u043c\u0430\u043b\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|h|<\/span><\/span>.\n<\/p>\n<p><a name=\"2\"><\/a><\/br><\/p>\n<h3>\u041a\u0440\u0438\u0442\u0435\u0440\u0438\u0439 \u043f\u0435\u0440\u0432\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439<\/h3>\n<p style=\"text-align: justify;\">\n  <a href=\"https:\/\/www.youtube.com\/watch?v=OscTlX3raaE&amp;t=1257s\" target=\"_blank\" rel=\"noopener\"><br \/>\n    <strong><span style=\"color: #ff0000;\">\u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043c\u044b \u0442\u043e\u043b\u044c\u043a\u043e \u0447\u0442\u043e \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043b\u0438,<\/span><\/strong><\/a> \u043c\u043e\u0436\u043d\u043e \u0441\u0432\u0435\u0441\u0442\u0438 \u043a \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0438\u043c\u043f\u043b\u0438\u043a\u0430\u0446\u0438\u0438:<\/p>\n<p style=\"text-align: center;\">\n  <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n  \\left\\{\\begin{matrix}f \\text{ \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442}\\\\ \\text{\u043b\u043e\u043a\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430 \u0432 }x_0 \\end{matrix}\\right\\}\n\n  \\Longrightarrow\n\n  \\left\\{\\begin{matrix} \\displaystyle f^\\prime(x_0) = 0 \\\\ \\\\ \\vee \\\\ \\\\ \\text{\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0432 }x_0 \\end{matrix}\\right\\}\n\n  <\/span><\/span>\n<\/p>\n<p style=\"text-align: justify;\">\n  \u0425\u043e\u0442\u044f \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0435\u043d\u0438\u0435 \u0432 \u043e\u0431\u0449\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043d\u0435\u0432\u0435\u0440\u043d\u043e, \u043e\u043d\u043e \u0432\u0435\u0441\u044c\u043c\u0430 \u043f\u043e\u043b\u0435\u0437\u043d\u043e \u0434\u043b\u044f \u0441\u0443\u0436\u0435\u043d\u0438\u044f \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043f\u043e\u0438\u0441\u043a\u0430 \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u043e\u0432. \u0418\u0441\u0445\u043e\u0434\u044f \u0438\u0437 \u044d\u0442\u043e\u0433\u043e, \u0432\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0442\u043e\u0447\u0435\u043a \u043f\u0435\u0440\u0432\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439.\n<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #e0ffe0;\">\n<p style=\"text-align: justify;\">\n          <span style=\"color: #000080;\"><strong>\u041e\u041f\u0420\u0415\u0414\u0415\u041b\u0415\u041d\u0418\u0415:<\/strong><\/span><br \/>\n          \u0413\u043e\u0432\u043e\u0440\u044f\u0442, \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <strong>\u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0442\u043e\u0447\u043a\u043e\u0439 \u043f\u0435\u0440\u0432\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439<\/strong>, \u0435\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x_0)=0<\/span><\/span> \u0438\u043b\u0438 \u0435\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x_0)<\/span><\/span> \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442.\n        <\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\n  \u041a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0432\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0432\u0430\u0436\u043d\u044b \u043f\u043e\u0442\u043e\u043c\u0443, \u0447\u0442\u043e \u043b\u044e\u0431\u0430\u044f \u0442\u043e\u0447\u043a\u0430, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430 (\u043b\u043e\u043a\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0438\u043b\u0438 \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0433\u043e), \u0434\u043e\u043b\u0436\u043d\u0430 \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0442\u044c \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0443 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0442\u043e\u0447\u0435\u043a:\n<\/p>\n<p style=\"text-align: center;\">\n  <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\left\\{\\begin{matrix}\\text{\u0442\u043e\u0447\u043a\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435}\\\\ \\text{\u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u044b\u043c\u0438 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430\u043c\u0438}\\end{matrix}\\right\\}\n\n  \\subseteq\n\n  \\left\\{\\begin{matrix}\\text{\u0442\u043e\u0447\u043a\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435}\\\\ \\text{\u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430\u043c\u0438}\\end{matrix}\\right\\}\n\n  \\subseteq\n\n  \\left\\{\\begin{matrix}\\text{\u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438}\\\\ \\text{\u043f\u0435\u0440\u0432\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439}\\end{matrix}\\right\\}\n\n  <\/span><\/span>\n<\/p>\n<p style=\"text-align: justify;\">\n  \u042d\u0442\u043e \u0438 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <strong>\u043a\u0440\u0438\u0442\u0435\u0440\u0438\u0435\u043c \u043f\u0435\u0440\u0432\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439<\/strong>, \u043f\u043e\u043d\u0438\u043c\u0430\u0435\u043c\u044b\u043c \u043a\u0430\u043a \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043e\u0432\u0430\u043d\u0438\u044f \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u043e\u0432 \u0432\u043e \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u0438\u0445 \u0442\u043e\u0447\u043a\u0430\u0445.\n<\/p>\n<p><a name=\"3\"><\/a><\/br><\/p>\n<h2>\u0422\u0435\u043e\u0440\u0435\u043c\u0430 \u0420\u043e\u043b\u043b\u044f<\/h2>\n<p style=\"text-align: justify;\">\n  <a href=\"https:\/\/www.youtube.com\/watch?v=OscTlX3raaE&amp;t=1454s\" target=\"_blank\" rel=\"noopener\"><br \/>\n    <strong><span style=\"color: #ff0000;\">\u041c\u044b \u0443\u0436\u0435 \u0432\u0438\u0434\u0435\u043b\u0438, \u0447\u0442\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/span><\/strong><\/a> \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0442\u043e\u0447\u0435\u043a \u043f\u0435\u0440\u0432\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0438\u0433\u0440\u0430\u0435\u0442 \u043a\u043b\u044e\u0447\u0435\u0432\u0443\u044e \u0440\u043e\u043b\u044c \u043f\u0440\u0438 \u043f\u043e\u0438\u0441\u043a\u0435 \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u043e\u0432. \u0412 \u0441\u0432\u044f\u0437\u0438 \u0441 \u044d\u0442\u0438\u043c \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u044c, \u043f\u0440\u0438 \u043a\u0430\u043a\u0438\u0445 \u0443\u0441\u043b\u043e\u0432\u0438\u044f\u0445 \u043c\u043e\u0436\u043d\u043e \u0433\u0430\u0440\u0430\u043d\u0442\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043e\u0432\u0430\u043d\u0438\u0435 \u0442\u0430\u043a\u0438\u0445 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0442\u043e\u0447\u0435\u043a. \u041f\u0440\u043e\u0434\u0432\u0438\u0436\u0435\u043d\u0438\u0435 \u0432 \u044d\u0442\u043e\u043c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u0434\u0430\u0435\u0442 \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u0420\u043e\u043b\u043b\u044f.<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #ffe0e0;\">\n<p style=\"text-align: justify;\">\n          <span style=\"color: #800000;\"><strong>\u0422\u0415\u041e\u0420\u0415\u041c\u0410:<\/strong><\/span><br \/>\n          \u041f\u0443\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u0430\u044f \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430\u044f \u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430\u044f \u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span>. \u0415\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(a)=f(b)<\/span><\/span>, \u0442\u043e \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]a,b[<\/span><\/span> \u0442\u0430\u043a\u043e\u0435, \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c)=0<\/span><\/span>.\n        <\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #e0e0ff;\">\n<p style=\"text-align: justify;\">\n          <span style=\"color: #000080;\"><strong>\u0414\u041e\u041a\u0410\u0417\u0410\u0422\u0415\u041b\u042c\u0421\u0422\u0412\u041e:<\/strong><\/span><br \/>\n          \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0434\u0432\u0430 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0445 \u0441\u043b\u0443\u0447\u0430\u044f:\n        <\/p>\n<ol style=\"text-align: justify;\">\n<li>\n            \u0415\u0441\u043b\u0438 \u0434\u043b\u044f \u0432\u0441\u0435\u0445 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in]a,b[<\/span><\/span> \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=f(a)=f(b)<\/span><\/span>, \u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u043e\u0439 \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x)=0<\/span><\/span> \u0434\u043b\u044f \u0432\u0441\u0435\u0445 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in]a,b[<\/span><\/span>. \u0412 \u0447\u0430\u0441\u0442\u043d\u043e\u0441\u0442\u0438, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]a,b[<\/span><\/span> \u0442\u0430\u043a\u043e\u0435, \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c)=0<\/span><\/span>.\n          <\/li>\n<li>\n            \u0415\u0441\u043b\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in]a,b[<\/span><\/span> \u0442\u0430\u043a\u043e\u0435, \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)\\neq f(a)=f(b)<\/span><\/span>, \u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u043d\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u043e\u0439. \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span>, \u043f\u043e \u0442\u0435\u043e\u0440\u0435\u043c\u0435 \u0412\u0435\u0439\u0435\u0440\u0448\u0442\u0440\u0430\u0441\u0441\u0430 \u043e\u043d\u0430 \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442 \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0433\u043e \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u0430 \u0438 \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0433\u043e \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u0430 \u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span>.<\/p>\n<p>\u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0442\u0430\u043a \u043a\u0430\u043a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(a)=f(b)<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u043d\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u043e\u0439, \u043f\u043e \u043a\u0440\u0430\u0439\u043d\u0435\u0439 \u043c\u0435\u0440\u0435 \u043e\u0434\u0438\u043d \u0438\u0437 \u044d\u0442\u0438\u0445 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u043e\u0432 \u0434\u043e\u043b\u0436\u0435\u043d \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0442\u044c\u0441\u044f \u0432\u043e \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u0435\u0439 \u0442\u043e\u0447\u043a\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span>.<\/p>\n<p>\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0435\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]a,b[<\/span><\/span> \u2014 \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u044f\u044f \u0442\u043e\u0447\u043a\u0430, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442 \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430, \u0442\u043e, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430 \u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span>, \u0432 \u0447\u0430\u0441\u0442\u043d\u043e\u0441\u0442\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c)<\/span><\/span>, \u0438 \u043f\u043e \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u0435 \u0437\u0430\u043a\u043b\u044e\u0447\u0430\u0435\u043c, \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c)=0<\/span><\/span>.\n          <\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"4\"><\/a><\/br><\/p>\n<h2>\u0422\u0435\u043e\u0440\u0435\u043c\u0430 \u043e \u0441\u0440\u0435\u0434\u043d\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0438 \u0434\u043b\u044f \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0438\u0441\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f<\/h2>\n<p style=\"text-align: justify;\">\n  <a href=\"https:\/\/www.youtube.com\/watch?v=OscTlX3raaE&amp;t=1878s\" target=\"_blank\" rel=\"noopener\"><br \/>\n    <strong><span style=\"color: #ff0000;\">\u0415\u0449\u0435 \u043e\u0434\u0438\u043d \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442, \u044f\u0432\u043b\u044f\u044e\u0449\u0438\u0439\u0441\u044f \u043f\u0440\u044f\u043c\u044b\u043c \u0441\u043b\u0435\u0434\u0441\u0442\u0432\u0438\u0435\u043c<\/span><\/strong><\/a> \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043d\u043d\u044b\u0445 \u0432\u044b\u0448\u0435 \u0442\u0435\u043e\u0440\u0435\u043c \u0438 \u043f\u0440\u0435\u0434\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0449\u0438\u0439 \u043f\u043e\u043b\u0435\u0437\u043d\u0443\u044e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044e \u0434\u043b\u044f \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u2014 \u044d\u0442\u043e \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u043e \u0441\u0440\u0435\u0434\u043d\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0438 \u0432 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u043c \u0438\u0441\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0438.\n<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #ffe0e0;\">\n<p style=\"text-align: justify;\">\n          <span style=\"color: #800000;\"><strong>\u0422\u0415\u041e\u0420\u0415\u041c\u0410:<\/strong><\/span><br \/>\n          \u041f\u0443\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u0430\u044f \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430\u044f \u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430\u044f \u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span>. \u0422\u043e\u0433\u0434\u0430 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]a,b[<\/span><\/span> \u0442\u0430\u043a\u043e\u0435, \u0447\u0442\u043e:\n        <\/p>\n<p style=\"text-align: center;\">\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c) =\\displaystyle \\frac{f(b) - f(a)}{b-a}<\/span><\/span>\n        <\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #e0e0ff;\">\n<p style=\"text-align: justify;\">\n          <span style=\"color: #000080;\"><strong>\u0414\u041e\u041a\u0410\u0417\u0410\u0422\u0415\u041b\u042c\u0421\u0422\u0412\u041e:<\/strong><\/span><br \/>\n          \u041f\u0443\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u0430\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439:\n        <\/p>\n<p style=\"text-align: center;\">\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(x) = f(x) - \\displaystyle \\frac{f(b) - f(a)}{b-a}(x-a)<\/span><\/span>\n        <\/p>\n<p style=\"text-align: justify;\">\n          \u042d\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430 \u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span>, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0442\u0430\u043a\u0438\u043c\u0438 \u0436\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u043c\u0438 \u043e\u0431\u043b\u0430\u0434\u0430\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span>. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(a)=F(b)<\/span><\/span>, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0442\u0435\u043e\u0440\u0435\u043c\u0443 \u0420\u043e\u043b\u043b\u044f \u0438 \u0437\u0430\u043a\u043b\u044e\u0447\u0438\u0442\u044c, \u0447\u0442\u043e \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0442\u043e\u0447\u043a\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]a,b[<\/span><\/span> \u0442\u0430\u043a\u0430\u044f, \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F^\\prime(c)=0<\/span><\/span>.\n        <\/p>\n<p style=\"text-align: justify;\">\n          \u0422\u0435\u043f\u0435\u0440\u044c, \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span>, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:\n        <\/p>\n<p style=\"text-align: center;\">\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F^\\prime(x) = f^\\prime(x) - \\displaystyle\\frac{f(b) - f(a)}{b-a}<\/span><\/span>\n        <\/p>\n<p style=\"text-align: justify;\">\n          \u041f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c<\/span><\/span> \u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F^\\prime(c)=0<\/span><\/span>, \u0438\u043c\u0435\u0435\u043c:\n        <\/p>\n<p style=\"text-align: center;\">\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0=F^\\prime(c) = f^\\prime(c) - \\displaystyle\\frac{f(b) - f(a)}{b-a}<\/span><\/span>\n        <\/p>\n<p style=\"text-align: justify;\">\n          \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e,\n        <\/p>\n<p style=\"text-align: center;\">\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c) = \\displaystyle\\frac{f(b) - f(a)}{b-a}<\/span><\/span>\n        <\/p>\n<p style=\"text-align: justify;\">\n          \u0447\u0442\u043e \u0438 \u0442\u0440\u0435\u0431\u043e\u0432\u0430\u043b\u043e\u0441\u044c \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u044c.\n        <\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"5\"><\/a><\/br><\/p>\n<h3>\u0418\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u044b \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u044f \u0438 \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u044f<\/h3>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #ffe0e0;\">\n<p style=\"text-align: justify;\">\n          <span style=\"color: #800000;\"><strong>\u0422\u0415\u041e\u0420\u0415\u041c\u0410:<\/strong><\/span>\n        <\/p>\n<ul style=\"text-align: justify;\">\n<li>\n            <a href=\"https:\/\/www.youtube.com\/watch?v=OscTlX3raaE&amp;t=2402s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0415\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f<\/span><\/strong><\/a>, \u0442\u0430\u043a\u0430\u044f \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall x\\in ]a,b[)\\left(0\\lt f^\\prime(x)\\right)<\/span><\/span>, \u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u0442\u0440\u043e\u0433\u043e \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u044e\u0449\u0435\u0439 \u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span>.\n          <\/li>\n<li>\n            \u0415\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0442\u0430\u043a\u0430\u044f \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall x\\in ]a,b[)\\left(f^\\prime(x)\\lt 0\\right)<\/span><\/span>, \u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u0442\u0440\u043e\u0433\u043e \u0443\u0431\u044b\u0432\u0430\u044e\u0449\u0435\u0439 \u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span>.\n          <\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #e0e0ff;\">\n<p style=\"text-align: justify;\">\n          <span style=\"color: #000080;\"><strong>\u0414\u041e\u041a\u0410\u0417\u0410\u0422\u0415\u041b\u042c\u0421\u0422\u0412\u041e:<\/strong><\/span><br \/>\n          \u041f\u0443\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1,x_2\\in ]a,b[<\/span><\/span> \u0442\u0430\u043a\u043e\u0432\u044b, \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1 \\lt x_2<\/span><\/span>. \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430 \u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span>, \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0442\u0435\u043e\u0440\u0435\u043c\u0443 \u043e \u0441\u0440\u0435\u0434\u043d\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0438 \u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u043d\u0430 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[x_1,x_2]\\subset ]a,b[<\/span><\/span>. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0442\u043e\u0447\u043a\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]x_1,x_2[<\/span><\/span> \u0442\u0430\u043a\u0430\u044f, \u0447\u0442\u043e:\n        <\/p>\n<p style=\"text-align: center;\">\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c) = \\displaystyle\\frac{f(x_2) - f(x_1)}{x_2 - x_1}<\/span><\/span>\n        <\/p>\n<p style=\"text-align: justify;\">\n          \u0418\u0437 \u044d\u0442\u043e\u0433\u043e \u0441\u043b\u0435\u0434\u0443\u0435\u0442:\n        <\/p>\n<ul style=\"text-align: justify;\">\n<li>\n            \u0415\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c) \\gt 0<\/span><\/span>, \u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x_2) - f(x_1) = f^\\prime(c)(x_2 - x_1) \\gt 0<\/span><\/span>.<br \/>\n\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442.\n          <\/li>\n<li>\n            \u0415\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c) \\lt 0<\/span><\/span>, \u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x_2) - f(x_1) = f^\\prime(c)(x_2 - x_1) \\lt 0<\/span><\/span>.<br \/>\n\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0443\u0431\u044b\u0432\u0430\u0435\u0442.\n          <\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\n\u0418\u0437\u0443\u0447\u0435\u043d\u0438\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u0432 \u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432 \u2014 \u044d\u0442\u043e \u043d\u0435 \u043f\u0440\u043e\u0441\u0442\u043e \u00ab\u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445\u00bb, \u0430 \u043e\u0441\u0432\u043e\u0435\u043d\u0438\u0435 \u0443\u043c\u0435\u043d\u0438\u044f \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0430\u0442\u044c \u0440\u0430\u0441\u043f\u043b\u044b\u0432\u0447\u0430\u0442\u044b\u0439 \u043f\u043e\u0438\u0441\u043a \u0432 \u043f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u0443 \u0441 \u0433\u0430\u0440\u0430\u043d\u0442\u0438\u044f\u043c\u0438 \u0438 \u0447\u0435\u0442\u043a\u0438\u043c\u0438 \u043a\u0440\u0438\u0442\u0435\u0440\u0438\u044f\u043c\u0438. \u0422\u0435\u043e\u0440\u0435\u043c\u0430 \u0412\u0435\u0439\u0435\u0440\u0448\u0442\u0440\u0430\u0441\u0441\u0430 \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442, \u043a\u043e\u0433\u0434\u0430 \u043c\u043e\u0436\u043d\u043e \u0431\u044b\u0442\u044c \u0443\u0432\u0435\u0440\u0435\u043d\u043d\u044b\u043c \u0432 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043e\u0432\u0430\u043d\u0438\u0438 \u043e\u043f\u0442\u0438\u043c\u0443\u043c\u0430 \u043d\u0430 \u043a\u043e\u043c\u043f\u0430\u043a\u0442\u043d\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435, \u0442\u043e\u0433\u0434\u0430 \u043a\u0430\u043a \u043a\u0440\u0438\u0442\u0435\u0440\u0438\u0439 \u043f\u0435\u0440\u0432\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439, \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u0420\u043e\u043b\u043b\u044f \u0438 \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u043e \u0441\u0440\u0435\u0434\u043d\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0438 \u0434\u0430\u044e\u0442 \u043a\u0430\u0440\u0442\u0443 \u0434\u043b\u044f \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u043a\u0430\u043d\u0434\u0438\u0434\u0430\u0442\u043e\u0432 \u0438 \u043e\u0431\u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u0432\u044b\u0432\u043e\u0434\u043e\u0432: \u0433\u0434\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043c\u043e\u0436\u0435\u0442 \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0442\u044c \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430, \u043a\u043e\u0433\u0434\u0430 \u044d\u0442\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438\u0448\u044c \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u043c, \u0438 \u043a\u0430\u043a \u0437\u043d\u0430\u043a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f&#039;<\/span><\/span> \u0432\u044b\u044f\u0432\u043b\u044f\u0435\u0442 \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u043d\u0438\u0435 \u0438 \u0443\u0431\u044b\u0432\u0430\u043d\u0438\u0435. \u041e\u0441\u0432\u043e\u0438\u0432 \u044d\u0442\u0443 \u0446\u0435\u043f\u043e\u0447\u043a\u0443 \u0438\u0434\u0435\u0439, \u0432\u044b \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u0442\u0435 \u043e\u0442 \u0438\u043d\u0442\u0443\u0438\u0442\u0438\u0432\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u043d\u0438\u044f \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432 \u043a \u0440\u0435\u0448\u0435\u043d\u0438\u044e \u0437\u0430\u0434\u0430\u0447 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0441 \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u0435\u043c\u044b\u043c\u0438 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430\u043c\u0438, \u0447\u0442\u043e \u0438 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0442\u043e\u0447\u043d\u0443\u044e \u0440\u0430\u0437\u043d\u0438\u0446\u0443 \u043c\u0435\u0436\u0434\u0443 \u00ab\u044f \u0434\u0443\u043c\u0430\u044e, \u0447\u0442\u043e \u043b\u0443\u0447\u0448\u0438\u0439 \u043f\u0443\u043d\u043a\u0442 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0437\u0434\u0435\u0441\u044c\u00bb \u0438 \u00ab\u044f \u0437\u043d\u0430\u044e, \u043f\u043e\u0447\u0435\u043c\u0443 \u043e\u043d \u0434\u043e\u043b\u0436\u0435\u043d \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u044c\u0441\u044f \u0438\u043c\u0435\u043d\u043d\u043e \u0437\u0434\u0435\u0441\u044c\u00bb.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u041c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u044b \u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0413\u0434\u0435 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u00ab\u043d\u0430\u0438\u043b\u0443\u0447\u0448\u0430\u044f\u00bb \u0442\u043e\u0447\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438: \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c, \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u0432\u044b \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0435\u0441\u044c \u0434\u043e\u0441\u0442\u0438\u0447\u044c, \u0438\u043b\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c, \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0438\u0437\u0431\u0435\u0436\u0430\u0442\u044c? \u042d\u0442\u043e\u0442 \u0432\u043e\u043f\u0440\u043e\u0441, \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u044e\u0449\u0438\u0439 \u0432 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438, \u0444\u0438\u0437\u0438\u043a\u0435, \u044d\u043a\u043e\u043d\u043e\u043c\u0438\u043a\u0435 \u0438 \u0438\u043d\u0436\u0435\u043d\u0435\u0440\u0438\u0438, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0434\u043d\u0438\u043c \u0438\u0437 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0445 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0439 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0438\u0441\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f. \u0418 \u0432\u043e\u0442 \u043a\u043b\u044e\u0447\u0435\u0432\u043e\u0439 \u043c\u043e\u043c\u0435\u043d\u0442: \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u0412\u0435\u0439\u0435\u0440\u0448\u0442\u0440\u0430\u0441\u0441\u0430 \u0433\u0430\u0440\u0430\u043d\u0442\u0438\u0440\u0443\u0435\u0442, \u0447\u0442\u043e \u0435\u0441\u043b\u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u0438 \u0432\u044b \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442\u0435 \u043d\u0430 \u0437\u0430\u043c\u043a\u043d\u0443\u0442\u043e\u043c \u0438 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435, \u0442\u043e \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u044b\u0435 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":35349,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":0,"footnotes":""},"categories":[864,573],"tags":[],"class_list":["post-35381","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-864","category-573"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u041c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u044b \u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u041e\u0441\u0432\u043e\u0439\u0442\u0435 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u044b \u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u044b \u0441 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