{"id":35376,"date":"2025-01-01T13:00:28","date_gmt":"2025-01-01T13:00:28","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=35376"},"modified":"2025-12-14T23:25:34","modified_gmt":"2025-12-14T23:25:34","slug":"%e0%a4%95%e0%a4%bf%e0%a4%b8%e0%a5%80-%e0%a4%ab%e0%a4%b2%e0%a4%a8-%e0%a4%95%e0%a5%87-%e0%a4%85%e0%a4%a7%e0%a4%bf%e0%a4%95%e0%a4%a4%e0%a4%ae-%e0%a4%94%e0%a4%b0-%e0%a4%a8%e0%a5%8d%e0%a4%af%e0%a5%82","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%95%e0%a4%bf%e0%a4%b8%e0%a5%80-%e0%a4%ab%e0%a4%b2%e0%a4%a8-%e0%a4%95%e0%a5%87-%e0%a4%85%e0%a4%a7%e0%a4%bf%e0%a4%95%e0%a4%a4%e0%a4%ae-%e0%a4%94%e0%a4%b0-%e0%a4%a8%e0%a5%8d%e0%a4%af%e0%a5%82\/","title":{"rendered":"\u0915\u093f\u0938\u0940 \u092b\u0932\u0928 \u0915\u0947 \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e"},"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>\u0915\u093f\u0938\u0940 \u092b\u0932\u0928 \u0915\u0947 \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e<\/h1>\n<p style=\"text-align:center\"><em>\u0915\u093f\u0938\u0940 \u092b\u0932\u0928 \u0915\u093e \u201c\u0938\u0930\u094d\u0935\u0936\u094d\u0930\u0947\u0937\u094d\u0920\u201d \u092c\u093f\u0902\u0926\u0941 \u0915\u0939\u093e\u0901 \u0939\u094b\u0924\u093e \u0939\u0948: \u0935\u0939 \u0905\u0927\u093f\u0915\u0924\u092e \u091c\u093f\u0938\u0947 \u0906\u092a \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902 \u092f\u093e \u0935\u0939 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u091c\u093f\u0938\u0947 \u0906\u092a\u0915\u094b \u091f\u093e\u0932\u0928\u093e \u0939\u0948? \u092f\u0939 \u092a\u094d\u0930\u0936\u094d\u0928, \u091c\u094b \u0905\u0928\u0941\u0915\u0942\u0932\u0928, \u092d\u094c\u0924\u093f\u0915\u0940, \u0905\u0930\u094d\u0925\u0936\u093e\u0938\u094d\u0924\u094d\u0930 \u0914\u0930 \u0905\u092d\u093f\u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915\u0940 \u092e\u0947\u0902 \u0926\u093f\u0916\u093e\u0908 \u0926\u0947\u0924\u093e \u0939\u0948, \u0905\u0935\u0915\u0932\u0928 \u0917\u0923\u093f\u0924 \u0915\u0947 \u092e\u0941\u0916\u094d\u092f \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u090f\u0915 \u0939\u0948\u0964 \u0914\u0930 \u092f\u0939\u093e\u0901 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092c\u093e\u0924 \u0906\u0924\u0940 \u0939\u0948: <a href=\"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%af%e0%a4%b0%e0%a4%b8%e0%a5%8d%e0%a4%9f%e0%a5%8d%e0%a4%b0%e0%a4%be%e0%a4%b8-%e0%a4%95%e0%a4%be-%e0%a4%9a%e0%a4%b0%e0%a4%ae-%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%aa%e0%a5%8d\/\" rel=\"noopener\" target=\"_blank\">\u0935\u093e\u0907\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u0915\u093e \u092a\u094d\u0930\u092e\u0947\u092f<\/a> \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0938\u0924\u0924 \u0939\u0948 \u0914\u0930 \u0906\u092a \u090f\u0915 \u092c\u0902\u0926 \u0924\u0925\u093e \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0905\u0902\u0924\u0930\u093e\u0932 \u092a\u0930 \u0915\u093e\u0930\u094d\u092f \u0915\u0930 \u0930\u0939\u0947 \u0939\u0948\u0902, \u0924\u094b <strong>\u092a\u0930\u092e \u091a\u0930\u092e \u092e\u093e\u0928 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902<\/strong>\u0964 \u0907\u0938\u0915\u0947 \u092c\u093e\u0926 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0935\u094d\u092f\u093e\u0935\u0939\u093e\u0930\u093f\u0915 \u0939\u094b \u091c\u093e\u0924\u0940 \u0939\u0948: <strong>\u0906\u0932\u094b\u091a\u0928\u093e\u0924\u094d\u092e\u0915 \u092c\u093f\u0902\u0926\u0941\u0913\u0902<\/strong> (<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f&#039;(x)=0<\/span><\/span> \u092f\u093e \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0928\u0939\u0940\u0902) \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 <strong>\u0938\u094d\u0925\u093e\u0928\u0940\u092f \u091a\u0930\u092e \u092e\u093e\u0928\u094b\u0902<\/strong> \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0930\u0928\u093e, \u0914\u0930 \u0930\u094b\u0932 \u0924\u0925\u093e \u092e\u093e\u0927\u094d\u092f \u092e\u093e\u0928 \u092a\u094d\u0930\u092e\u0947\u092f \u091c\u0948\u0938\u0947 \u0909\u092a\u0915\u0930\u0923\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u201c\u0905\u0902\u0927\u0940\u201d \u0916\u094b\u091c \u0915\u094b \u090f\u0915 \u0938\u094d\u092a\u0937\u094d\u091f, \u0938\u0924\u094d\u092f\u093e\u092a\u0928 \u092f\u094b\u0917\u094d\u092f \u0914\u0930 \u0915\u0941\u0936\u0932 \u0935\u093f\u0927\u093f \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u093f\u0924 \u0915\u0930\u0928\u093e\u0964<\/em><\/p>\n<p style=\"text-align:center\">\n<strong>\u0905\u0927\u093f\u0917\u092e \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f:<\/strong>\n<\/p>\n<ol>\n<li><b>\u0928\u093f\u0937\u094d\u092a\u093e\u0926\u093f\u0924 \u0915\u0930\u0928\u093e<\/b> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u092e\u0947\u0902 \u092a\u0930\u092e \u091a\u0930\u092e \u092e\u093e\u0928 \u0916\u094b\u091c\u0928\u0947 \u0915\u0940 \u090f\u0915 \u092a\u0942\u0930\u094d\u0923 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e: \u0906\u0902\u0924\u0930\u093f\u0915 \u0906\u0932\u094b\u091a\u0928\u093e\u0924\u094d\u092e\u0915 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0924\u0925\u093e \u0905\u0902\u0924\u0930\u093e\u0932 \u0915\u0947 \u0938\u093f\u0930\u094b\u0902 \u092a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0915\u093e \u092e\u093e\u0928 \u0928\u093f\u0915\u093e\u0932\u0928\u093e, \u0914\u0930 \u0905\u0927\u093f\u0915\u0924\u092e \u0924\u0925\u093e \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u092a\u0930\u092e \u092e\u093e\u0928 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u0939\u0947\u0924\u0941 \u092e\u093e\u0928\u094b\u0902 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0928\u093e\u0964\n  <\/li>\n<li><strong>\u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0928\u093e<\/strong> \u0906\u0935\u0936\u094d\u092f\u0915 \u0936\u0930\u094d\u0924 \u092c\u0928\u093e\u092e \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0936\u0930\u094d\u0924 \u0915\u0947 \u092e\u093e\u0928 \u0915\u0940: \u092f\u0939 \u092a\u0939\u091a\u093e\u0928\u0928\u093e \u0915\u093f \u201c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f&#039;(x_0)=0<\/span><\/span>\u201d \u0938\u094d\u0925\u093e\u0928\u0940\u092f \u091a\u0930\u092e \u092e\u093e\u0928 \u0915\u0940 \u0917\u093e\u0930\u0902\u091f\u0940 \u0928\u0939\u0940\u0902 \u0926\u0947\u0924\u093e, \u0914\u0930 \u092f\u0939 \u0924\u092f \u0915\u0930\u0928\u093e \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902 \u0915\u094c\u0928 \u0938\u0947 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u092a\u094d\u0930\u092e\u093e\u0923 (\u092e\u093e\u0928\u094b\u0902 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e, \u0938\u0902\u0915\u0947\u0924\u094b\u0902 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923, \u0938\u094d\u0925\u093e\u0928\u0940\u092f \u0935\u094d\u092f\u0935\u0939\u093e\u0930) \u0909\u092a\u092f\u0941\u0915\u094d\u0924 \u0939\u0948\u0902\u0964\n  <\/li>\n<li><strong>\u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0928\u093e<\/strong> \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u0947 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0938\u092c\u0938\u0947 \u0915\u0941\u0936\u0932 \u0930\u0923\u0928\u0940\u0924\u093f: \u0938\u0918\u0928 \u0905\u0902\u0924\u0930\u093e\u0932\u094b\u0902 \u092e\u0947\u0902 \u092a\u0930\u092e \u091a\u0930\u092e \u092e\u093e\u0928 (\u0935\u093e\u0907\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 + \u0938\u0940\u092e\u093f\u0924 \u092e\u0942\u0932\u094d\u092f\u093e\u0902\u0915\u0928) \u092c\u0928\u093e\u092e \u0906\u0902\u0924\u0930\u093f\u0915 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u092a\u0930 \u0938\u094d\u0925\u093e\u0928\u0940\u092f \u091a\u0930\u092e \u092e\u093e\u0928 (\u0906\u0932\u094b\u091a\u0928\u093e\u0924\u094d\u092e\u0915 \u092c\u093f\u0902\u0926\u0941 + \u0938\u094d\u0925\u093e\u0928\u0940\u092f \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923), \u0914\u0930 \u091a\u092f\u0928 \u0915\u093e \u0914\u091a\u093f\u0924\u094d\u092f \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0928\u093e\u0964\n  <\/li>\n<\/ol>\n<p style=\"text-align:center;\">\n<strong><u>\u0935\u093f\u0937\u092f\u0935\u0938\u094d\u0924\u0941 \u0938\u0942\u091a\u0915\u093e\u0902\u0915<\/u>:<\/strong><br \/>\n<a href=\"#1\"><strong>\u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e, \u092a\u0930\u092e \u0914\u0930 \u0938\u094d\u0925\u093e\u0928\u0940\u092f \u091a\u0930\u092e \u092e\u093e\u0928<\/strong><\/a><br \/>\n<a href=\"#2\">\u092a\u094d\u0930\u0925\u092e \u0905\u0935\u0915\u0932\u091c \u0915\u093e \u092e\u093e\u0928\u0926\u0902\u0921<\/a><br \/>\n<a href=\"#3\"><strong>\u0930\u094b\u0932 \u0915\u093e \u092a\u094d\u0930\u092e\u0947\u092f<\/strong><\/a><br \/>\n<a href=\"#4\"><strong>\u0905\u0935\u0915\u0932\u0928 \u0915\u093e \u092e\u093e\u0927\u094d\u092f \u092e\u093e\u0928 \u092a\u094d\u0930\u092e\u0947\u092f<\/strong><\/a><br \/>\n<a href=\"#5\">\u0935\u0943\u0926\u094d\u0927\u093f \u0914\u0930 \u0939\u094d\u0930\u093e\u0938 \u0915\u0947 \u0905\u0902\u0924\u0930\u093e\u0932<\/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\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%af%e0%a4%b0%e0%a4%b8%e0%a5%8d%e0%a4%9f%e0%a5%8d%e0%a4%b0%e0%a4%be%e0%a4%b8-%e0%a4%95%e0%a4%be-%e0%a4%9a%e0%a4%b0%e0%a4%ae-%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%aa%e0%a5%8d\/\" rel=\"noopener\" target=\"_blank\">\u0935\u093e\u0907\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u0915\u093e \u092a\u094d\u0930\u092e\u0947\u092f<\/a> \u0939\u092e\u0947\u0902 \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u092f\u0926\u093f \u0915\u094b\u0908 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u092e\u093e\u0928 \u0935\u093e\u0932\u093e \u092b\u0932\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span> \u0915\u0947 \u0915\u093f\u0938\u0940 \u092c\u0902\u0926 \u0914\u0930 \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0909\u092a\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u092a\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0924\u0925\u093e \u0938\u0924\u0924 \u0939\u0948, \u0924\u094b \u0935\u0939 \u0905\u0928\u093f\u0935\u093e\u0930\u094d\u092f \u0930\u0942\u092a \u0938\u0947 \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u092e\u093e\u0928 (\u092a\u0930\u092e \u091a\u0930\u092e \u092e\u093e\u0928) \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0915\u093f\u0938\u0940 \u092b\u0932\u0928 \u0915\u0947 \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0915\u0940 \u0916\u094b\u091c \u0915\u094b <strong>\u0905\u0928\u0941\u0915\u0942\u0932\u0928 \u0938\u092e\u0938\u094d\u092f\u093e<\/strong> \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u0935\u093e\u0907\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u0915\u093e \u092a\u094d\u0930\u092e\u0947\u092f \u0939\u092e\u0947\u0902 \u092f\u0939 \u0917\u093e\u0930\u0902\u091f\u0940 \u0926\u0947\u0924\u093e \u0939\u0948 \u0915\u093f \u091c\u092c \u092d\u0940 \u092b\u0932\u0928 \u0938\u0924\u0924 \u0939\u094b \u0914\u0930 \u0921\u094b\u092e\u0947\u0928 \u0938\u0918\u0928 \u0939\u094b, \u0924\u092c \u092a\u0930\u092e \u091a\u0930\u092e \u092e\u093e\u0928\u094b\u0902 \u0915\u0947 \u0905\u0930\u094d\u0925 \u092e\u0947\u0902 \u0938\u092e\u093e\u0927\u093e\u0928 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0939\u094b \u091c\u093e\u0928\u0947 \u0915\u0947 \u092c\u093e\u0926, \u0905\u092c \u0915\u0947\u0935\u0932 \u0910\u0938\u0940 \u0930\u0923\u0928\u0940\u0924\u093f\u092f\u093e\u0901 \u0935\u093f\u0915\u0938\u093f\u0924 \u0915\u0930\u0928\u093e \u0936\u0947\u0937 \u0930\u0939\u0924\u093e \u0939\u0948 \u091c\u094b \u0907\u0928 \u0938\u092e\u093e\u0927\u093e\u0928\u094b\u0902 \u0915\u094b \u0916\u094b\u091c\u0928\u0947 \u092e\u0947\u0902 \u0938\u0939\u093e\u092f\u0915 \u0939\u094b\u0902\u0964\n<\/p>\n<p><a name=\"1\"><\/a><\/br><\/p>\n<h2>\u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e, \u092a\u0930\u092e \u0924\u0925\u093e \u0938\u094d\u0925\u093e\u0928\u0940\u092f \u091a\u0930\u092e \u092e\u093e\u0928<\/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;\">\u0938\u092e\u0940\u0915\u094d\u0937\u093e \u092a\u094d\u0930\u093e\u0930\u0902\u092d \u0915\u0930\u0928\u0947 \u0938\u0947 \u092a\u0939\u0932\u0947<\/span><\/a> \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0915\u0940 \u0916\u094b\u091c \u0915\u0940 \u0930\u0923\u0928\u0940\u0924\u093f\u092f\u094b\u0902 \u092a\u0930, \u092f\u0939 \u0938\u094d\u092a\u0937\u094d\u091f \u0930\u0942\u092a \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930 \u0932\u0947\u0902 \u0915\u093f \u0939\u092e \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u0915\u094d\u092f\u093e \u0916\u094b\u091c\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902\u0964\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>\u092a\u0930\u093f\u092d\u093e\u0937\u093e:<\/strong><\/span><br \/>\n          \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u090f\u0915 \u092b\u0932\u0928 \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0921\u094b\u092e\u0947\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D<\/span><\/span> \u0939\u0948\u0964 \u0939\u092e \u0915\u0939\u0947\u0902\u0917\u0947 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u092c\u093f\u0902\u0926\u0941 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in D<\/span><\/span> \u092a\u0930 <strong>\u092a\u0930\u092e \u0905\u0927\u093f\u0915\u0924\u092e<\/strong> \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u092f\u0926\u093f:\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          \u0914\u0930 \u0935\u0939 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u092a\u0930 <strong>\u092a\u0930\u092e \u0928\u094d\u092f\u0942\u0928\u0924\u092e<\/strong> \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0947\u0917\u093e \u092f\u0926\u093f:\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  \u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u094d\u0925\u093e\u0928\u0940\u092f \u091a\u0930\u092e \u092e\u093e\u0928 (\u0921\u094b\u092e\u0947\u0928 \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937) \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964\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>\u092a\u0930\u093f\u092d\u093e\u0937\u093e:<\/strong><\/span><br \/>\n          \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u090f\u0915 \u092b\u0932\u0928 \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0921\u094b\u092e\u0947\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D<\/span><\/span> \u0939\u0948 \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in D<\/span><\/span>\u0964 \u0939\u092e \u0915\u0939\u0947\u0902\u0917\u0947 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u092c\u093f\u0902\u0926\u0941 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u092a\u0930 <strong>\u0938\u094d\u0925\u093e\u0928\u0940\u092f \u0905\u0927\u093f\u0915\u0924\u092e<\/strong> \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u092f\u0926\u093f:\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          \u0914\u0930 \u0935\u0939 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u092a\u0930 <strong>\u0938\u094d\u0925\u093e\u0928\u0940\u092f \u0928\u094d\u092f\u0942\u0928\u0924\u092e<\/strong> \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0947\u0917\u093e \u092f\u0926\u093f:\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  \u0907\u0938\u0938\u0947 \u0939\u092e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u094b \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:\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>\u092a\u094d\u0930\u092e\u0947\u092f:<\/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;\">\u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u090f\u0915 \u092c\u093f\u0902\u0926\u0941 \u0939\u0948<\/span><\/strong><\/a> \u091c\u094b \u090f\u0915 \u0938\u0918\u0928 \u0905\u0902\u0924\u0930\u093e\u0932 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/span> \u0915\u0947 \u0906\u0902\u0924\u0930\u093f\u0915 \u092d\u093e\u0917 \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0924 \u0939\u0948\u0964 \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u092c\u093f\u0902\u0926\u0941 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u092a\u0930 \u090f\u0915 <strong>\u0938\u094d\u0925\u093e\u0928\u0940\u092f<\/strong> \u0905\u0927\u093f\u0915\u0924\u092e \u092f\u093e \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x_0)<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948, \u0924\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x_0)=0<\/span><\/span> \u0939\u094b\u0917\u093e\u0964\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>\u092a\u094d\u0930\u092e\u093e\u0923:<\/strong><\/span><br \/>\n          \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u092c\u093f\u0902\u0926\u0941 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u092a\u0930 \u090f\u0915 \u0938\u094d\u0925\u093e\u0928\u0940\u092f \u0905\u0927\u093f\u0915\u0924\u092e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0924\u092c \u0915\u094b\u0908 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h_0 \\gt 0<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948 \u0910\u0938\u093e \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f, \u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|h|\\lt h_0<\/span><\/span> \u0939\u094b \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0+h\\in I<\/span><\/span> \u0939\u094b, \u092f\u0939 \u0938\u0924\u094d\u092f \u0939\u0948 \u0915\u093f:\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          \u091c\u094b \u0915\u093f \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u092f \u0939\u0948:\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          \u0905\u092c \u0939\u092e \u0926\u094b \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0930\u0947\u0902:\n        <\/p>\n<ul>\n<li>\n<p style=\"text-align: justify;\">\n              \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h&gt;0<\/span><\/span> \u0939\u094b, \u0924\u094b:\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              \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h\\lt 0<\/span><\/span> \u0939\u094b, \u0924\u094b:\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          \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x_0)<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948, \u0924\u094b \u091c\u092c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h\\to 0<\/span><\/span> \u0939\u094b, \u0924\u092c \u0935\u0943\u0926\u094d\u0927\u093f \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u0940 \u0938\u0940\u092e\u093e \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u094b\u0924\u0940 \u0939\u0948 \u0914\u0930 \u0909\u0938\u0947 \u0926\u094b\u0928\u094b\u0902 \u0905\u0938\u092e\u093e\u0928\u0924\u093e\u0913\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0938\u0902\u0917\u0924 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f, \u091c\u093f\u0938\u0938\u0947 \u092f\u0939 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f:\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          \u092f\u0939\u0940 \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0925\u093e\u0964\n        <\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\n  \u092f\u0939 \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0928\u093e \u091a\u093e\u0939\u093f\u090f \u0915\u093f \u092f\u0939 \u092a\u094d\u0930\u092e\u093e\u0923 \u0938\u094d\u0925\u093e\u0928\u0940\u092f \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0915\u0947 \u0932\u093f\u090f \u092d\u0940 \u092e\u093e\u0928\u094d\u092f \u0939\u0948\u0964 \u0909\u0938 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902 \u0906\u0930\u0902\u092d \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x_0+h)\\ge f(x_0)<\/span><\/span> \u0938\u0947, \u091c\u092c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|h|<\/span><\/span> \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0930\u0942\u092a \u0938\u0947 \u091b\u094b\u091f\u093e \u0939\u094b\u0964\n<\/p>\n<p><a name=\"2\"><\/a><\/br><\/p>\n<h3>\u092a\u094d\u0930\u0925\u092e \u0905\u0935\u0915\u0932\u091c \u0915\u093e \u092e\u093e\u0928\u0926\u0902\u0921<\/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;\">\u091c\u093f\u0938 \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u0940 \u0939\u092e\u0928\u0947 \u0905\u092d\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0940 \u0939\u0948<\/span><\/strong><\/a> \u0909\u0938\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0928\u093f\u0939\u093f\u0924\u093e\u0930\u094d\u0925 \u092e\u0947\u0902 \u0938\u0902\u0915\u094d\u0937\u0947\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:\n<\/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{ \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u093e \u0939\u0948}\\\\ \\text{ }x_0 \\text{ \u092a\u0930 \u090f\u0915 \u0938\u094d\u0925\u093e\u0928\u0940\u092f \u091a\u0930\u092e}\\end{matrix}\\right\\}\n\n  \\Longrightarrow\n\n  \\left\\{\\begin{matrix} \\displaystyle f^\\prime(x_0) = 0 \\\\ \\\\ \\vee \\\\ \\\\ \\text{ }x_0 \\text{ \u092a\u0930 \u0905\u0935\u0915\u0932\u091c \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0928\u0939\u0940\u0902 \u0939\u0948}\\end{matrix}\\right\\}\n\n  <\/span><\/span>\n<\/p>\n<p style=\"text-align: justify;\">\n  \u092f\u0926\u094d\u092f\u092a\u093f \u0907\u0938 \u0928\u093f\u0939\u093f\u0924\u093e\u0930\u094d\u0925 \u0915\u093e \u0935\u094d\u092f\u0941\u0924\u094d\u0915\u094d\u0930\u092e \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0924\u0903 \u0938\u0924\u094d\u092f \u0928\u0939\u0940\u0902 \u0939\u0948, \u092b\u093f\u0930 \u092d\u0940 \u092f\u0939 \u0938\u094d\u0925\u093e\u0928\u0940\u092f \u091a\u0930\u092e \u092e\u093e\u0928\u094b\u0902 \u0915\u0940 \u0916\u094b\u091c \u0915\u094b \u0938\u0940\u092e\u093f\u0924 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0905\u0924\u094d\u092f\u0902\u0924 \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u0948\u0964 \u0907\u0938\u0940 \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u092a\u094d\u0930\u0925\u092e \u0905\u0935\u0915\u0932\u091c \u0915\u0947 \u0906\u0932\u094b\u091a\u0928\u093e\u0924\u094d\u092e\u0915 \u092c\u093f\u0902\u0926\u0941 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964\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>\u092a\u0930\u093f\u092d\u093e\u0937\u093e:<\/strong><\/span><br \/>\n          \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> <strong>\u092a\u094d\u0930\u0925\u092e \u0905\u0935\u0915\u0932\u091c \u0915\u093e \u090f\u0915 \u0906\u0932\u094b\u091a\u0928\u093e\u0924\u094d\u092e\u0915 \u092c\u093f\u0902\u0926\u0941<\/strong> \u0939\u0948 \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x_0)=0<\/span><\/span> \u0939\u094b \u092f\u093e \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x_0)<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0928 \u0939\u094b\u0964\n        <\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\n  \u092a\u094d\u0930\u0925\u092e \u0905\u0935\u0915\u0932\u091c \u0915\u0947 \u0906\u0932\u094b\u091a\u0928\u093e\u0924\u094d\u092e\u0915 \u092c\u093f\u0902\u0926\u0941 \u092e\u0939\u0924\u094d\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u091c\u0939\u093e\u0901 \u092d\u0940 \u092b\u0932\u0928 (\u0938\u094d\u0925\u093e\u0928\u0940\u092f \u092f\u093e \u092a\u0930\u092e \u0930\u0942\u092a \u0938\u0947) \u091a\u0930\u092e \u092e\u093e\u0928 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u093e \u0939\u0948, \u0935\u0939 \u092c\u093f\u0902\u0926\u0941 \u0906\u0932\u094b\u091a\u0928\u093e\u0924\u094d\u092e\u0915 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u092e\u0947\u0902 \u0905\u0935\u0936\u094d\u092f \u0938\u092e\u094d\u092e\u093f\u0932\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:\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{\u0935\u0947 \u092c\u093f\u0902\u0926\u0941 \u091c\u094b}\\\\ \\text{\u092a\u0930\u092e \u0930\u0942\u092a \u0938\u0947 \u091a\u0930\u092e \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902}\\end{matrix}\\right\\}\n\n  \\subseteq\n\n  \\left\\{\\begin{matrix}\\text{\u0935\u0947 \u092c\u093f\u0902\u0926\u0941 \u091c\u094b}\\\\ \\text{\u0938\u094d\u0925\u093e\u0928\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u091a\u0930\u092e \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902}\\end{matrix}\\right\\}\n\n  \\subseteq\n\n  \\left\\{\\begin{matrix}\\text{\u092a\u094d\u0930\u0925\u092e \u0905\u0935\u0915\u0932\u091c \u0915\u0947}\\\\ \\text{\u0906\u0932\u094b\u091a\u0928\u093e\u0924\u094d\u092e\u0915 \u092c\u093f\u0902\u0926\u0941}\\end{matrix}\\right\\}\n\n  <\/span><\/span>\n<\/p>\n<p style=\"text-align: justify;\">\n  \u0907\u0938\u0947 \u0939\u0940 \u0939\u092e <strong>\u092a\u094d\u0930\u0925\u092e \u0905\u0935\u0915\u0932\u091c \u0915\u093e \u092e\u093e\u0928\u0926\u0902\u0921<\/strong> \u0915\u0939\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0938\u0947 \u0906\u0902\u0924\u0930\u093f\u0915 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u092a\u0930 \u0938\u094d\u0925\u093e\u0928\u0940\u092f \u091a\u0930\u092e \u092e\u093e\u0928\u094b\u0902 \u0915\u0947 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0906\u0935\u0936\u094d\u092f\u0915 \u0936\u0930\u094d\u0924 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0938\u092e\u091d\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964\n<\/p>\n<p><a name=\"3\"><\/a><\/br><\/p>\n<h2>\u0930\u094b\u0932 \u0915\u093e \u092a\u094d\u0930\u092e\u0947\u092f<\/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;\">\u0939\u092e \u092a\u0939\u0932\u0947 \u0939\u0940 \u0926\u0947\u0916 \u091a\u0941\u0915\u0947 \u0939\u0948\u0902 \u0915\u093f<\/span><\/strong><\/a> \u092a\u094d\u0930\u0925\u092e \u0905\u0935\u0915\u0932\u091c \u0915\u0947 \u0906\u0932\u094b\u091a\u0928\u093e\u0924\u094d\u092e\u0915 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u093e \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u0923 \u0938\u094d\u0925\u093e\u0928\u0940\u092f \u091a\u0930\u092e \u092e\u093e\u0928\u094b\u0902 \u0915\u0940 \u0916\u094b\u091c \u092e\u0947\u0902 \u0905\u0924\u094d\u092f\u0902\u0924 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948\u0964 \u0907\u0938\u0940 \u0915\u093e\u0930\u0923 \u092f\u0939 \u0938\u094d\u0935\u093e\u092d\u093e\u0935\u093f\u0915 \u0939\u0948 \u0915\u093f \u092f\u0939 \u091c\u093e\u0901\u091a\u093e \u091c\u093e\u090f \u0915\u093f \u0915\u093f\u0928 \u092a\u0930\u093f\u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0910\u0938\u0947 \u0906\u0932\u094b\u091a\u0928\u093e\u0924\u094d\u092e\u0915 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u0915\u0940 \u0917\u093e\u0930\u0902\u091f\u0940 \u0926\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938 \u0926\u093f\u0936\u093e \u092e\u0947\u0902 \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092a\u094d\u0930\u0917\u0924\u093f \u0930\u094b\u0932 \u0915\u0947 \u092a\u094d\u0930\u092e\u0947\u092f \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964\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>\u092a\u094d\u0930\u092e\u0947\u092f:<\/strong><\/span><br \/>\n          \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u090f\u0915 \u092b\u0932\u0928 \u0939\u0948 \u091c\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u092a\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0914\u0930 \u0938\u0924\u0924 \u0939\u0948, \u0924\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u092a\u0930 \u0905\u0935\u0915\u0932\u0928\u0940\u092f \u0939\u0948\u0964 \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(a)=f(b)<\/span><\/span> \u0939\u094b, \u0924\u094b \u0910\u0938\u093e \u090f\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]a,b[<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948 \u091c\u093f\u0938\u0915\u0947 \u0932\u093f\u090f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c)=0<\/span><\/span> \u0939\u094b\u0924\u093e \u0939\u0948\u0964\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>\u092a\u094d\u0930\u092e\u093e\u0923:<\/strong><\/span><br \/>\n          \u0939\u092e \u0926\u094b \u0938\u0902\u092d\u093e\u0935\u0928\u093e\u0913\u0902 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0947\u0902\u0917\u0947:\n        <\/p>\n<ol style=\"text-align: justify;\">\n<li>\n            \u092f\u0926\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in]a,b[<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=f(a)=f(b)<\/span><\/span> \u0939\u094b, \u0924\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0938\u094d\u0925\u093f\u0930 \u0939\u0948 \u0914\u0930 \u092a\u0930\u093f\u0923\u093e\u092e\u0938\u094d\u0935\u0930\u0942\u092a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x)=0<\/span><\/span> \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in]a,b[<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947, \u0910\u0938\u093e \u090f\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]a,b[<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948 \u091c\u093f\u0938\u0915\u0947 \u0932\u093f\u090f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c)=0<\/span><\/span>\u0964\n          <\/li>\n<li>\n            \u092f\u0926\u093f \u0915\u094b\u0908 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in]a,b[<\/span><\/span> \u0910\u0938\u093e \u0939\u0948 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)\\neq f(a)=f(b)<\/span><\/span>, \u0924\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0938\u094d\u0925\u093f\u0930 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964 \u091a\u0942\u0901\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u092a\u0930 \u0938\u0924\u0924 \u0939\u0948, \u0935\u093e\u0907\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u0915\u0947 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0935\u0939 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u092a\u0930 \u090f\u0915 \u092a\u0930\u092e \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u090f\u0915 \u092a\u0930\u092e \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/p>\n<p>\u0907\u0938\u0915\u0947 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924, \u0915\u094d\u092f\u094b\u0902\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(a)=f(b)<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0938\u094d\u0925\u093f\u0930 \u0928\u0939\u0940\u0902 \u0939\u0948, \u0907\u0928 \u091a\u0930\u092e \u092e\u093e\u0928\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u0915\u092e \u0938\u0947 \u0915\u092e \u090f\u0915 \u0915\u093e \u0918\u091f\u093f\u0924 \u0939\u094b\u0928\u093e \u0906\u0902\u0924\u0930\u093f\u0915 \u092d\u093e\u0917 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u092e\u0947\u0902 \u0939\u0940 \u0939\u094b\u0917\u093e\u0964<\/p>\n<p>\u0905\u0924\u0903 \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]a,b[<\/span><\/span> \u090f\u0915 \u0906\u0902\u0924\u0930\u093f\u0915 \u092c\u093f\u0902\u0926\u0941 \u0939\u0948 \u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u090f\u0915 \u0938\u094d\u0925\u093e\u0928\u0940\u092f \u091a\u0930\u092e \u092e\u093e\u0928 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u091a\u0942\u0901\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u092a\u0930 \u0905\u0935\u0915\u0932\u0928\u0940\u092f \u0939\u0948, \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c)<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948, \u0914\u0930 \u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u093e\u0932\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c)=0<\/span><\/span>\u0964\n          <\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"4\"><\/a><\/br><\/p>\n<h2>\u0905\u0935\u0915\u0932\u0928 \u0915\u093e \u092e\u093e\u0927\u094d\u092f \u092e\u093e\u0928 \u092a\u094d\u0930\u092e\u0947\u092f<\/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;\">\u090f\u0915 \u0905\u0928\u094d\u092f \u092a\u0930\u093f\u0923\u093e\u092e, \u091c\u094b \u0905\u092d\u0940-\u0905\u092d\u0940 \u0926\u0947\u0916\u0947 \u0917\u090f \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u093e \u092a\u094d\u0930\u0924\u094d\u092f\u0915\u094d\u0937 \u092a\u0930\u093f\u0923\u093e\u092e \u0939\u0948<\/span><\/strong><\/a> \u0914\u0930 \u091c\u094b \u092b\u0932\u0928\u094b\u0902 \u0915\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u094b\u0917\u0940 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948, \u0935\u0939 \u0905\u0935\u0915\u0932\u0928 \u0915\u0947 \u0932\u093f\u090f \u092e\u093e\u0927\u094d\u092f \u092e\u093e\u0928 \u092a\u094d\u0930\u092e\u0947\u092f \u0939\u0948\u0964\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>\u092a\u094d\u0930\u092e\u0947\u092f:<\/strong><\/span><br \/>\n          \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u090f\u0915 \u092b\u0932\u0928 \u0939\u0948 \u091c\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u092a\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0914\u0930 \u0938\u0924\u0924 \u0939\u0948, \u0924\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u092a\u0930 \u0905\u0935\u0915\u0932\u0928\u0940\u092f \u0939\u0948\u0964 \u0924\u092c \u0910\u0938\u093e \u090f\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]a,b[<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948 \u0915\u093f:\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>\u092a\u094d\u0930\u092e\u093e\u0923:<\/strong><\/span><br \/>\n          \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> \u0935\u0939 \u092b\u0932\u0928 \u0939\u0948 \u091c\u093f\u0938\u0947 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948:\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          \u092f\u0939 \u092b\u0932\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u092a\u0930 \u0938\u0924\u0924 \u0939\u0948 \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u092a\u0930 \u0905\u0935\u0915\u0932\u0928\u0940\u092f \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u092d\u0940 \u0910\u0938\u093e \u0939\u0940 \u0939\u0948\u0964 \u0907\u0938\u0915\u0947 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(a)=F(b)<\/span><\/span> \u0939\u0948, \u0905\u0924\u0903 \u0939\u092e \u0930\u094b\u0932 \u0915\u0947 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u093e\u0932 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0910\u0938\u093e \u090f\u0915 \u092c\u093f\u0902\u0926\u0941 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]a,b[<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948 \u091c\u093f\u0938\u0915\u0947 \u0932\u093f\u090f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F^\\prime(c)=0<\/span><\/span>\u0964\n        <\/p>\n<p style=\"text-align: justify;\">\n          \u0905\u092c, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> \u0915\u093e \u0905\u0935\u0915\u0932\u0928 \u0915\u0930\u0928\u0947 \u092a\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:\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          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c<\/span><\/span> \u092a\u0930 \u092e\u093e\u0928 \u0928\u093f\u0915\u093e\u0932\u0924\u0947 \u0939\u0941\u090f \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F^\\prime(c)=0<\/span><\/span> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f:\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          \u0905\u0924\u0903:\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          \u092f\u0939\u0940 \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0925\u093e\u0964\n        <\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"5\"><\/a><\/br><\/p>\n<h3>\u0935\u0943\u0926\u094d\u0927\u093f \u0914\u0930 \u0939\u094d\u0930\u093e\u0938 \u0915\u0947 \u0905\u0902\u0924\u0930\u093e\u0932<\/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>\u092a\u094d\u0930\u092e\u0947\u092f:<\/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;\">\u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u090f\u0915 \u092b\u0932\u0928 \u0939\u0948<\/span><\/strong><\/a> \u0910\u0938\u093e \u0915\u093f <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>, \u0924\u092c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u092e\u0947\u0902 \u0938\u0916\u094d\u0924\u0940 \u0938\u0947 \u092c\u0922\u093c\u0928\u0947 \u0935\u093e\u0932\u093e \u0939\u0948\u0964\n          <\/li>\n<li>\n            \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u090f\u0915 \u092b\u0932\u0928 \u0939\u0948 \u0910\u0938\u093e \u0915\u093f <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>, \u0924\u092c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u092e\u0947\u0902 \u0938\u0916\u094d\u0924\u0940 \u0938\u0947 \u0918\u091f\u0928\u0947 \u0935\u093e\u0932\u093e \u0939\u0948\u0964\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>\u092a\u094d\u0930\u092e\u093e\u0923:<\/strong><\/span><br \/>\n          \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1,x_2\\in ]a,b[<\/span><\/span> \u0910\u0938\u0947 \u0939\u0948\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1 \\lt x_2<\/span><\/span>\u0964 \u091a\u0942\u0901\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u092e\u0947\u0902 \u0905\u0935\u0915\u0932\u0928\u0940\u092f \u0939\u0948, \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u092a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[x_1,x_2]\\subset ]a,b[<\/span><\/span> \u0905\u0902\u0924\u0930\u093e\u0932 \u092e\u0947\u0902 \u092e\u093e\u0927\u094d\u092f \u092e\u093e\u0928 \u092a\u094d\u0930\u092e\u0947\u092f \u0932\u093e\u0917\u0942 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u092a\u0930\u093f\u0923\u093e\u092e\u0938\u094d\u0935\u0930\u0942\u092a, \u0910\u0938\u093e \u090f\u0915 \u092c\u093f\u0902\u0926\u0941 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]x_1,x_2[<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948 \u0915\u093f:\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          \u0907\u0938\u0938\u0947:\n        <\/p>\n<ul style=\"text-align: justify;\">\n<li>\n            \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c) \\gt 0<\/span><\/span>, \u0924\u092c <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>\u0964<br \/>\n            \u0905\u0924\u0903 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u092c\u0922\u093c\u0928\u0947 \u0935\u093e\u0932\u093e \u0939\u0948\u0964\n          <\/li>\n<li>\n            \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c) \\lt 0<\/span><\/span>, \u0924\u092c <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>\u0964<br \/>\n            \u0905\u0924\u0903 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0918\u091f\u0928\u0947 \u0935\u093e\u0932\u093e \u0939\u0948\u0964\n          <\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\n\u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0947\u0935\u0932 \u201c\u0905\u0935\u0915\u0932\u091c \u0928\u093f\u0915\u093e\u0932\u0928\u093e\u201d \u092d\u0930 \u0928\u0939\u0940\u0902 \u0939\u0948, \u092c\u0932\u094d\u0915\u093f \u090f\u0915 \u0905\u0938\u094d\u092a\u0937\u094d\u091f \u0916\u094b\u091c \u0915\u094b \u0910\u0938\u0940 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u092e\u0947\u0902 \u0930\u0942\u092a\u093e\u0902\u0924\u0930\u093f\u0924 \u0915\u0930\u0928\u093e \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u0938\u094d\u092a\u0937\u094d\u091f \u092e\u093e\u0928\u0926\u0902\u0921 \u0914\u0930 \u0917\u093e\u0930\u0902\u091f\u093f\u092f\u093e\u0901 \u0939\u094b\u0902\u0964 \u0935\u093e\u0907\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u092f\u0939 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u092c \u0906\u092a \u092f\u0939 \u092d\u0930\u094b\u0938\u093e \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0915\u093f\u0938\u0940 \u0938\u0918\u0928 \u0905\u0902\u0924\u0930\u093e\u0932 \u092e\u0947\u0902 \u090f\u0915 \u0907\u0937\u094d\u091f\u0924\u092e \u092e\u093e\u0928 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948, \u091c\u092c\u0915\u093f \u092a\u094d\u0930\u0925\u092e \u0905\u0935\u0915\u0932\u091c \u0915\u093e \u092e\u093e\u0928\u0926\u0902\u0921, \u0930\u094b\u0932 \u0915\u093e \u092a\u094d\u0930\u092e\u0947\u092f \u0914\u0930 \u092e\u093e\u0927\u094d\u092f \u092e\u093e\u0928 \u092a\u094d\u0930\u092e\u0947\u092f \u0906\u092a\u0915\u094b \u092a\u094d\u0930\u0924\u094d\u092f\u093e\u0936\u093f\u092f\u094b\u0902 \u0915\u094b \u0916\u094b\u091c\u0928\u0947 \u0914\u0930 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937\u094b\u0902 \u0915\u094b \u0914\u091a\u093f\u0924\u094d\u092f \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0928\u0947 \u0915\u093e \u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930 \u0926\u0947\u0924\u0947 \u0939\u0948\u0902: \u0915\u093f\u0938\u0940 \u092b\u0932\u0928 \u0915\u093e \u091a\u0930\u092e \u0915\u0939\u093e\u0901 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948, \u0915\u092c \u0935\u0939 \u0936\u0930\u094d\u0924 \u0915\u0947\u0935\u0932 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u094b\u0924\u0940 \u0939\u0948, \u0914\u0930 \u0915\u0948\u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f&#039;<\/span><\/span> \u0915\u093e \u0938\u0902\u0915\u0947\u0924 \u0935\u0943\u0926\u094d\u0927\u093f \u0914\u0930 \u0939\u094d\u0930\u093e\u0938 \u0915\u094b \u092a\u094d\u0930\u0915\u091f \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u092f\u0926\u093f \u0906\u092a \u0907\u0938 \u0935\u093f\u091a\u093e\u0930-\u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e \u092e\u0947\u0902 \u0928\u093f\u092a\u0941\u0923 \u0939\u094b \u091c\u093e\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0906\u092a \u0915\u0947\u0935\u0932 \u0905\u0902\u0924\u0903\u092a\u094d\u0930\u0947\u0930\u0923\u093e \u0938\u0947 \u0917\u094d\u0930\u093e\u092b \u0926\u0947\u0916\u0928\u0947 \u0938\u0947 \u0906\u0917\u0947 \u092c\u0922\u093c\u0915\u0930 \u0938\u0924\u094d\u092f\u093e\u092a\u0928 \u092f\u094b\u0917\u094d\u092f \u0924\u0930\u094d\u0915\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0905\u0928\u0941\u0915\u0942\u0932\u0928 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0901 \u0939\u0932 \u0915\u0930\u0928\u0947 \u0932\u0917\u0924\u0947 \u0939\u0948\u0902, \u0914\u0930 \u092f\u0939\u0940 \u201c\u092e\u0941\u091d\u0947 \u0932\u0917\u0924\u093e \u0939\u0948 \u0915\u093f \u0938\u092c\u0938\u0947 \u0905\u091a\u094d\u091b\u093e \u092c\u093f\u0902\u0926\u0941 \u092f\u0939\u093e\u0901 \u0939\u0948\u201d \u0924\u0925\u093e \u201c\u092e\u0941\u091d\u0947 \u092a\u0924\u093e \u0939\u0948 \u0915\u093f \u0935\u0939 \u092f\u0939\u093e\u0901 \u0915\u094d\u092f\u094b\u0902 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u201d \u0915\u0947 \u092c\u0940\u091a \u0915\u093e \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0905\u0902\u0924\u0930 \u0939\u0948\u0964<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0915\u093f\u0938\u0940 \u092b\u0932\u0928 \u0915\u0947 \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0915\u093f\u0938\u0940 \u092b\u0932\u0928 \u0915\u093e \u201c\u0938\u0930\u094d\u0935\u0936\u094d\u0930\u0947\u0937\u094d\u0920\u201d \u092c\u093f\u0902\u0926\u0941 \u0915\u0939\u093e\u0901 \u0939\u094b\u0924\u093e \u0939\u0948: \u0935\u0939 \u0905\u0927\u093f\u0915\u0924\u092e \u091c\u093f\u0938\u0947 \u0906\u092a \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902 \u092f\u093e \u0935\u0939 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u091c\u093f\u0938\u0947 \u0906\u092a\u0915\u094b \u091f\u093e\u0932\u0928\u093e \u0939\u0948? \u092f\u0939 \u092a\u094d\u0930\u0936\u094d\u0928, \u091c\u094b \u0905\u0928\u0941\u0915\u0942\u0932\u0928, \u092d\u094c\u0924\u093f\u0915\u0940, \u0905\u0930\u094d\u0925\u0936\u093e\u0938\u094d\u0924\u094d\u0930 \u0914\u0930 \u0905\u092d\u093f\u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915\u0940 \u092e\u0947\u0902 \u0926\u093f\u0916\u093e\u0908 \u0926\u0947\u0924\u093e \u0939\u0948, \u0905\u0935\u0915\u0932\u0928 \u0917\u0923\u093f\u0924 \u0915\u0947 \u092e\u0941\u0916\u094d\u092f \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u090f\u0915 \u0939\u0948\u0964 \u0914\u0930 \u092f\u0939\u093e\u0901 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092c\u093e\u0924 \u0906\u0924\u0940 [&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":[862,577],"tags":[],"class_list":["post-35376","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-862","category-577"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0915\u093f\u0938\u0940 \u092b\u0932\u0928 \u0915\u0947 \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0905\u0935\u0915\u0932\u0928 \u0917\u0923\u093f\u0924 \u0915\u0940 \u090f\u0915 \u0906\u0927\u0941\u0928\u093f\u0915 \u0926\u0943\u0937\u094d\u091f\u093f \u0915\u0947 \u0938\u093e\u0925 \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 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Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/35376","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=35376"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/35376\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/35349"}],"wp:attachment":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=35376"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=35376"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=35376"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}