{"id":35401,"date":"2025-01-01T13:00:48","date_gmt":"2025-01-01T13:00:48","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=35401"},"modified":"2025-12-14T23:54:26","modified_gmt":"2025-12-14T23:54:26","slug":"%e9%96%a2%e6%95%b0%e3%81%ae%e6%9c%80%e5%a4%a7%e5%80%a4%e3%81%a8%e6%9c%80%e5%b0%8f%e5%80%a4","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ja\/%e9%96%a2%e6%95%b0%e3%81%ae%e6%9c%80%e5%a4%a7%e5%80%a4%e3%81%a8%e6%9c%80%e5%b0%8f%e5%80%a4\/","title":{"rendered":"\u95a2\u6570\u306e\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024"},"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>\u95a2\u6570\u306e\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024<\/h1>\n<p style=\"text-align:center\"><em>\u95a2\u6570\u306b\u304a\u3051\u308b\u300c\u6700\u826f\u300d\u306e\u70b9\u306f\u3069\u3053\u306b\u3042\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5230\u9054\u3057\u305f\u3044\u6700\u5927\u5024\u306a\u306e\u304b\uff0c\u305d\u308c\u3068\u3082\u907f\u3051\u308b\u3079\u304d\u6700\u5c0f\u5024\u306a\u306e\u304b\u3002\u3053\u306e\u554f\u3044\u306f\uff0c\u6700\u9069\u5316\uff0c\u7269\u7406\u5b66\uff0c\u7d4c\u6e08\u5b66\uff0c\u5de5\u5b66\u306b\u73fe\u308c\uff0c\u5fae\u5206\u7a4d\u5206\u5b66\u306e\u4e3b\u8981\u306a\u5fdc\u7528\u306e\u4e00\u3064\u3067\u3059\u3002\u3053\u3053\u3067\u91cd\u8981\u306a\u306e\u304c\uff0c<a href=\"https:\/\/toposuranos.com\/material\/ja\/weierstrass-%e3%81%ae%e6%a5%b5%e5%80%a4%e5%ae%9a%e7%90%86\/\" rel=\"noopener\" target=\"_blank\">\u30ef\u30a4\u30a8\u30eb\u30b7\u30e5\u30c8\u30e9\u30b9\u306e\u5b9a\u7406<\/a>\u3067\u3059\u3002\u3053\u306e\u5b9a\u7406\u306f\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u304c\u9023\u7d9a\u3067\uff0c\u9589\u533a\u9593\u304b\u3064\u6709\u754c\u306a\u533a\u9593\u4e0a\u3067\u8003\u3048\u308b\u306a\u3089\u3070\uff0c<strong>\u7d76\u5bfe\u7684\u306a\u6975\u5024\u304c\u5b58\u5728\u3059\u308b<\/strong>\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002\u305d\u3053\u304b\u3089\u8b70\u8ad6\u306f\u5b9f\u8df5\u7684\u306b\u306a\u308a\u307e\u3059\u3002\u3059\u306a\u308f\u3061\uff0c<strong>\u81e8\u754c\u70b9<\/strong>\uff08<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f&#039;(x)=0<\/span><\/span> \u307e\u305f\u306f\u5b58\u5728\u3057\u306a\u3044\u70b9\uff09\u3092\u7528\u3044\u3066 <strong>\u5c40\u6240\u7684\u6975\u5024<\/strong>\u3092\u691c\u51fa\u3057\uff0c\u30ed\u30eb\u306e\u5b9a\u7406\u3084\u5e73\u5747\u5024\u306e\u5b9a\u7406\u3068\u3044\u3063\u305f\u9053\u5177\u3092\u7528\u3044\u308b\u3053\u3068\u3067\uff0c\u300c\u624b\u63a2\u308a\u300d\u306e\u63a2\u7d22\u3092\uff0c\u660e\u78ba\u3067\u691c\u8a3c\u53ef\u80fd\u304b\u3064\u52b9\u7387\u7684\u306a\u65b9\u6cd5\u3078\u3068\u5909\u63db\u3059\u308b\u306e\u3067\u3059\u3002<\/em><\/p>\n<p style=\"text-align:center\">\n<strong>\u5b66\u7fd2\u76ee\u6a19:<\/strong>\n<\/p>\n<ol>\n<li><b>\u5b9f\u884c\u3059\u308b<\/b>\uff1a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u306b\u304a\u3051\u308b\u7d76\u5bfe\u7684\u6975\u5024\u3092\u6c42\u3081\u308b\u5b8c\u5168\u306a\u624b\u9806\u3002\u3059\u306a\u308f\u3061\uff0c\u533a\u9593\u5185\u90e8\u306e\u81e8\u754c\u70b9\u304a\u3088\u3073\u533a\u9593\u7aef\u70b9\u306b\u304a\u3044\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u3092\u8a55\u4fa1\u3057\uff0c\u5024\u3092\u6bd4\u8f03\u3057\u3066\u7d76\u5bfe\u6700\u5927\u5024\u3068\u7d76\u5bfe\u6700\u5c0f\u5024\u3092\u6c7a\u5b9a\u3059\u308b\u3002\n  <\/li>\n<li><strong>\u5bfe\u6bd4\u3059\u308b<\/strong>\uff1a\u5fc5\u8981\u6761\u4ef6\u3068\u5341\u5206\u6761\u4ef6\u306e\u9055\u3044\u3002\u3059\u306a\u308f\u3061\uff0c\u300c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f&#039;(x_0)=0<\/span><\/span>\u300d\u304c\u5c40\u6240\u7684\u6975\u5024\u3092\u4fdd\u8a3c\u3057\u306a\u3044\u3053\u3068\u3092\u8a8d\u8b58\u3057\uff0c\u5404\u5834\u5408\u306b\u304a\u3044\u3066\u3069\u306e\u8ffd\u52a0\u7684\u8a3c\u62e0\uff08\u5024\u306e\u6bd4\u8f03\uff0c\u7b26\u53f7\u89e3\u6790\uff0c\u5c40\u6240\u7684\u6319\u52d5\uff09\u304c\u9069\u5207\u304b\u3092\u5224\u65ad\u3059\u308b\u3002\n  <\/li>\n<li><strong>\u6c7a\u5b9a\u3059\u308b<\/strong>\uff1a\u554f\u984c\u306e\u7a2e\u985e\u306b\u5fdc\u3058\u3066\u6700\u3082\u52b9\u7387\u7684\u306a\u6226\u7565\u3002\u30b3\u30f3\u30d1\u30af\u30c8\u533a\u9593\u306b\u304a\u3051\u308b\u7d76\u5bfe\u7684\u6975\u5024\uff08\u30ef\u30a4\u30a8\u30eb\u30b7\u30e5\u30c8\u30e9\u30b9\uff0b\u6709\u9650\u56de\u306e\u8a55\u4fa1\uff09\u3068\uff0c\u5185\u90e8\u70b9\u306b\u304a\u3051\u308b\u5c40\u6240\u7684\u6975\u5024\uff08\u81e8\u754c\u70b9\uff0b\u5c40\u6240\u89e3\u6790\uff09\u3092\u533a\u5225\u3057\uff0c\u9078\u629e\u3092\u6b63\u5f53\u5316\u3059\u308b\u3002\n  <\/li>\n<\/ol>\n<p style=\"text-align:center;\">\n<strong><u>\u5185\u5bb9\u7d22\u5f15<\/u>:<\/strong><br \/>\n<a href=\"#1\"><strong>\u6700\u5927\u5024\u30fb\u6700\u5c0f\u5024\uff0c\u7d76\u5bfe\u7684\u6975\u5024\u3068\u5c40\u6240\u7684\u6975\u5024<\/strong><\/a><br \/>\n<a href=\"#2\">\u4e00\u6b21\u5c0e\u95a2\u6570\u306e\u5224\u5b9a\u57fa\u6e96<\/a><br \/>\n<a href=\"#3\"><strong>\u30ed\u30eb\u306e\u5b9a\u7406<\/strong><\/a><br \/>\n<a href=\"#4\"><strong>\u5fae\u5206\u306e\u5e73\u5747\u5024\u306e\u5b9a\u7406<\/strong><\/a><br \/>\n<a href=\"#5\">\u5897\u52a0\u533a\u9593\u3068\u6e1b\u5c11\u533a\u9593<\/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\/ja\/weierstrass-%e3%81%ae%e6%a5%b5%e5%80%a4%e5%ae%9a%e7%90%86\/\" rel=\"noopener\" target=\"_blank\">\u30ef\u30a4\u30a8\u30eb\u30b7\u30e5\u30c8\u30e9\u30b9\u306e\u5b9a\u7406<\/a>\u306f\uff0c\u5b9f\u6570\u5024\u95a2\u6570\u304c <span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span> \u306e\u9589\u304b\u3064\u6709\u754c\u306a\u90e8\u5206\u96c6\u5408\u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\uff0c\u304b\u3064\u9023\u7d9a\u3067\u3042\u308b\u306a\u3089\u3070\uff0c\u5fc5\u305a\u6700\u5927\u5024\u304a\u3088\u3073\u6700\u5c0f\u5024\uff08\u7d76\u5bfe\u7684\u6975\u5024\uff09\u3092\u53d6\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002\u95a2\u6570\u306e\u6700\u5927\u5024\u30fb\u6700\u5c0f\u5024\u3092\u63a2\u3059\u3053\u3068\u306f <strong>\u6700\u9069\u5316\u554f\u984c<\/strong> \u3068\u547c\u3070\u308c\uff0c\u30ef\u30a4\u30a8\u30eb\u30b7\u30e5\u30c8\u30e9\u30b9\u306e\u5b9a\u7406\u306f\uff0c\u95a2\u6570\u304c\u9023\u7d9a\u3067\u5b9a\u7fa9\u57df\u304c\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3042\u308b\u9650\u308a\uff0c\u7d76\u5bfe\u7684\u6975\u5024\u3068\u3044\u3046\u610f\u5473\u3067\u89e3\u306e\u5b58\u5728\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002\u5b58\u5728\u304c\u4fdd\u8a3c\u3055\u308c\u305f\u4eca\uff0c\u3042\u3068\u306f\u305d\u308c\u3089\u306e\u89e3\u3092\u898b\u3064\u3051\u308b\u305f\u3081\u306e\u6226\u7565\u3092\u69cb\u7bc9\u3059\u308b\u3060\u3051\u3067\u3059\u3002\n<\/p>\n<p><a name=\"1\"><\/a><\/br><\/p>\n<h2>\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\uff0c\u7d76\u5bfe\u7684\u6975\u5024\u3068\u5c40\u6240\u7684\u6975\u5024<\/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;\">\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u306e\u63a2\u7d22<\/span><\/a>\u306b\u95a2\u3059\u308b\u6226\u7565\u3092\u691c\u8a0e\u3059\u308b\u524d\u306b\uff0c\u307e\u305a\u4f55\u3092\u6c42\u3081\u305f\u3044\u306e\u304b\u3092\u660e\u78ba\u306b\u5b9a\u7fa9\u3057\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/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>\u5b9a\u7fa9:<\/strong><\/span><br \/>\n<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D<\/span><\/span> \u3092\u5b9a\u7fa9\u57df\u3068\u3059\u308b\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u3092\u8003\u3048\u308b\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in D<\/span><\/span> \u306b\u304a\u3044\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u304c <strong>\u7d76\u5bfe\u6700\u5927\u5024<\/strong> \u3092\u53d6\u308b\u3068\u306f\uff0c\u6b21\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u3044\u3046\u3002\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          \u307e\u305f\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u306b\u304a\u3044\u3066 <strong>\u7d76\u5bfe\u6700\u5c0f\u5024<\/strong> \u3092\u53d6\u308b\u3068\u306f\uff0c\u6b21\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3067\u3042\u308b\u3002\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  \u540c\u69d8\u306b\u3057\u3066\uff0c\u5c40\u6240\u7684\u6975\u5024\uff08\u5b9a\u7fa9\u57df\u306b\u76f8\u5bfe\u7684\u306a\u6982\u5ff5\uff09\u3082\u5b9a\u7fa9\u3055\u308c\u308b\u3002\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>\u5b9a\u7fa9:<\/strong><\/span><br \/>\n          \u5b9a\u7fa9\u57df <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D<\/span><\/span> \u3092\u3082\u3064\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u3068\u70b9 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in D<\/span><\/span> \u3092\u8003\u3048\u308b\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u306b\u304a\u3044\u3066 <strong>\u5c40\u6240\u6700\u5927\u5024<\/strong> \u3092\u53d6\u308b\u3068\u306f\uff0c\u6b21\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u3044\u3046\u3002\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          \u307e\u305f\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u306b\u304a\u3044\u3066 <strong>\u5c40\u6240\u6700\u5c0f\u5024<\/strong> \u3092\u53d6\u308b\u3068\u306f\uff0c\u6b21\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3067\u3042\u308b\u3002\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  \u3053\u308c\u3088\u308a\uff0c\u6b21\u306e\u7d50\u679c\u3092\u8ff0\u3079\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\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>\u5b9a\u7406:<\/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;\">\u70b9 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u3092\u8003\u3048\u308b<\/span><\/strong><\/a>\u3002\u3053\u308c\u306f\u30b3\u30f3\u30d1\u30af\u30c8\u533a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/span> \u306e\u5185\u90e8\u70b9\u3067\u3042\u308b\u3002\u3082\u3057 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u306b\u304a\u3044\u3066 <strong>\u5c40\u6240\u7684<\/strong> \u306a\u6700\u5927\u5024\u307e\u305f\u306f\u6700\u5c0f\u5024\u3092\u53d6\u308a\uff0c\u304b\u3064 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x_0)<\/span><\/span> \u304c\u5b58\u5728\u3059\u308b\u306a\u3089\u3070\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x_0)=0<\/span><\/span> \u304c\u6210\u308a\u7acb\u3064\u3002\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>\u8a3c\u660e:<\/strong><\/span><br \/>\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u306b\u304a\u3044\u3066\u5c40\u6240\u6700\u5927\u5024\u3092\u53d6\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3002\u3053\u306e\u3068\u304d\uff0c\u3042\u308b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h_0 \\gt 0<\/span><\/span> \u304c\u5b58\u5728\u3057\u3066\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|h|\\lt h_0<\/span><\/span> \u304b\u3064 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0+h\\in I<\/span><\/span> \u3092\u6e80\u305f\u3059\u3059\u3079\u3066\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h<\/span><\/span> \u306b\u5bfe\u3057\u3066\uff0c\u6b21\u304c\u6210\u308a\u7acb\u3064\u3002\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          \u3053\u308c\u306f\u6b21\u3068\u540c\u5024\u3067\u3042\u308b\u3002\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          \u3053\u3053\u3067\uff0c\u6b21\u306e\u4e8c\u3064\u306e\u5834\u5408\u3092\u8003\u3048\u308b\u3002\n        <\/p>\n<ul>\n<li>\n<p style=\"text-align: justify;\">\n              <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h&gt;0<\/span><\/span> \u306e\u5834\u5408\uff1a\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              <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h\\lt 0<\/span><\/span> \u306e\u5834\u5408\uff1a\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          \u3082\u3057 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x_0)<\/span><\/span> \u304c\u5b58\u5728\u3059\u308b\u306a\u3089\u3070\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h\\to 0<\/span><\/span> \u306e\u3068\u304d\u306e\u5dee\u5546\u306e\u6975\u9650\u304c\u5b58\u5728\u3057\uff0c\u304b\u3064\u4e21\u65b9\u306e\u4e0d\u7b49\u5f0f\u3068\u6574\u5408\u7684\u3067\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3002\u3053\u306e\u3053\u3068\u304b\u3089\uff0c\u6b21\u304c\u5fc5\u7136\u7684\u306b\u5f93\u3046\u3002\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          \u4ee5\u4e0a\u3067\u8a3c\u660e\u3055\u308c\u305f\u3002\n        <\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\n  \u3053\u306e\u8a3c\u660e\u306f\uff0c\u5c40\u6240\u6700\u5c0f\u5024\u306e\u5834\u5408\u306b\u3082\u540c\u69d8\u306b\u6210\u308a\u7acb\u3064\u3053\u3068\u306b\u6ce8\u610f\u3059\u3079\u304d\u3067\u3042\u308b\u3002\u305d\u306e\u5834\u5408\u306f\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|h|<\/span><\/span> \u304c\u5341\u5206\u5c0f\u3055\u3044\u3068\u304d\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x_0+h)\\ge f(x_0)<\/span><\/span> \u304b\u3089\u51fa\u767a\u3059\u308b\u3002\n<\/p>\n<p><a name=\"2\"><\/a><\/br><\/p>\n<h3>\u4e00\u6b21\u5c0e\u95a2\u6570\u306e\u5224\u5b9a\u57fa\u6e96<\/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;\">\u5148\u307b\u3069\u78ba\u8a8d\u3057\u305f\u7d50\u679c<\/span><\/strong><\/a>\u306f\uff0c\u6b21\u306e\u542b\u610f\u3068\u3057\u3066\u8981\u7d04\u3067\u304d\u308b\u3002\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{ \u304c}\\\\ \\text{ }x_0\\text{ \u306b\u304a\u3044\u3066\u5c40\u6240\u7684\u6975\u5024\u3092\u53d6\u308b} \\end{matrix}\\right\\}\n\n  \\Longrightarrow\n\n  \\left\\{\\begin{matrix} \\displaystyle f^\\prime(x_0) = 0 \\\\ \\\\ \\vee \\\\ \\\\ x_0\\text{ \u306b\u304a\u3044\u3066\u5c0e\u95a2\u6570\u304c\u5b58\u5728\u3057\u306a\u3044} \\end{matrix}\\right\\}\n\n  <\/span><\/span>\n<\/p>\n<p style=\"text-align: justify;\">\n  \u3053\u306e\u542b\u610f\u306e\u9006\u306f\u4e00\u822c\u306b\u306f\u6210\u308a\u7acb\u305f\u306a\u3044\u304c\uff0c\u5c40\u6240\u7684\u6975\u5024\u306e\u63a2\u7d22\u7bc4\u56f2\u3092\u7d5e\u308a\u8fbc\u3080\u4e0a\u3067\u975e\u5e38\u306b\u6709\u7528\u3067\u3042\u308b\u3002\u3053\u306e\u8003\u3048\u65b9\u306b\u57fa\u3065\u3044\u3066\uff0c\u4e00\u6b21\u5c0e\u95a2\u6570\u306e\u81e8\u754c\u70b9\u304c\u5b9a\u7fa9\u3055\u308c\u308b\u3002\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>\u5b9a\u7fa9:<\/strong><\/span><br \/>\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u304c <strong>\u4e00\u6b21\u5c0e\u95a2\u6570\u306e\u81e8\u754c\u70b9<\/strong> \u3067\u3042\u308b\u3068\u306f\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x_0)=0<\/span><\/span> \u3067\u3042\u308b\u304b\uff0c\u307e\u305f\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x_0)<\/span><\/span> \u304c\u5b58\u5728\u3057\u306a\u3044\u3053\u3068\u3092\u3044\u3046\u3002\n        <\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\n  \u4e00\u6b21\u5c0e\u95a2\u6570\u306e\u81e8\u754c\u70b9\u304c\u91cd\u8981\u3067\u3042\u308b\u306e\u306f\uff0c\u95a2\u6570\u304c\u6975\u5024\uff08\u5c40\u6240\u7684\u307e\u305f\u306f\u7d76\u5bfe\u7684\uff09\u3092\u53d6\u308b\u3059\u3079\u3066\u306e\u70b9\u304c\uff0c\u5fc5\u305a\u81e8\u754c\u70b9\u306e\u96c6\u5408\u306b\u542b\u307e\u308c\u308b\u304b\u3089\u3067\u3042\u308b\u3002\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{\u7d76\u5bfe\u7684\u306b}\\\\ \\text{\u6975\u5024\u3092\u53d6\u308b\u70b9}\\end{matrix}\\right\\}\n\n  \\subseteq\n\n  \\left\\{\\begin{matrix}\\text{\u5c40\u6240\u7684\u306b}\\\\ \\text{\u6975\u5024\u3092\u53d6\u308b\u70b9}\\end{matrix}\\right\\}\n\n  \\subseteq\n\n  \\left\\{\\begin{matrix}\\text{\u4e00\u6b21\u5c0e\u95a2\u6570\u306e}\\\\ \\text{\u81e8\u754c\u70b9}\\end{matrix}\\right\\}\n\n  <\/span><\/span>\n<\/p>\n<p style=\"text-align: justify;\">\n  \u3053\u308c\u304c\uff0c\u5185\u90e8\u70b9\u306b\u304a\u3051\u308b\u5c40\u6240\u7684\u6975\u5024\u306e\u5b58\u5728\u306b\u5bfe\u3059\u308b\u5fc5\u8981\u6761\u4ef6\u3068\u3057\u3066\u7406\u89e3\u3055\u308c\u308b <strong>\u4e00\u6b21\u5c0e\u95a2\u6570\u306e\u5224\u5b9a\u57fa\u6e96<\/strong> \u3067\u3042\u308b\u3002\n<\/p>\n<p><a name=\"3\"><\/a><\/br><\/p>\n<h2>\u30ed\u30eb\u306e\u5b9a\u7406<\/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;\">\u3059\u3067\u306b\u898b\u305f\u3088\u3046\u306b<\/span><\/strong><\/a>\uff0c\u4e00\u6b21\u5c0e\u95a2\u6570\u306e\u81e8\u754c\u70b9\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u306f\u5c40\u6240\u7684\u6975\u5024\u306e\u63a2\u7d22\u306b\u304a\u3044\u3066\u91cd\u8981\u3067\u3042\u308b\u3002\u305d\u306e\u305f\u3081\uff0c\u3069\u306e\u3088\u3046\u306a\u6761\u4ef6\u306e\u4e0b\u3067\u305d\u306e\u3088\u3046\u306a\u81e8\u754c\u70b9\u306e\u5b58\u5728\u304c\u4fdd\u8a3c\u3055\u308c\u308b\u306e\u304b\u3092\u691c\u8a0e\u3059\u308b\u3053\u3068\u306f\u81ea\u7136\u3067\u3042\u308b\u3002\u3053\u306e\u65b9\u5411\u306b\u304a\u3051\u308b\u91cd\u8981\u306a\u524d\u9032\u304c\uff0c\u30ed\u30eb\u306e\u5b9a\u7406\u3067\u3042\u308b\u3002\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>\u5b9a\u7406:<\/strong><\/span><br \/>\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u9023\u7d9a\u306a\u95a2\u6570\u3068\u3057\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u4e0a\u3067\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308b\u3068\u3059\u308b\u3002\u3082\u3057 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(a)=f(b)<\/span><\/span> \u3067\u3042\u308c\u3070\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]a,b[<\/span><\/span> \u304c\u5b58\u5728\u3057\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c)=0<\/span><\/span> \u3068\u306a\u308b\u3002\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>\u8a3c\u660e:<\/strong><\/span><br \/>\n          \u6b21\u306e\u4e8c\u3064\u306e\u5834\u5408\u3092\u8003\u3048\u308b\u3002\n        <\/p>\n<ol style=\"text-align: justify;\">\n<li>\n            \u3059\u3079\u3066\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in]a,b[<\/span><\/span> \u306b\u5bfe\u3057\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=f(a)=f(b)<\/span><\/span> \u304c\u6210\u308a\u7acb\u3064\u5834\u5408\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u306f\u5b9a\u6570\u95a2\u6570\u3067\u3042\u308a\uff0c\u3057\u305f\u304c\u3063\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(x)=0<\/span><\/span> \u304c\u3059\u3079\u3066\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in]a,b[<\/span><\/span> \u3067\u6210\u308a\u7acb\u3064\u3002\u7279\u306b\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]a,b[<\/span><\/span> \u304c\u5b58\u5728\u3057\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c)=0<\/span><\/span> \u3068\u306a\u308b\u3002\n          <\/li>\n<li>\n            \u3042\u308b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in]a,b[<\/span><\/span> \u304c\u5b58\u5728\u3057\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)\\neq f(a)=f(b)<\/span><\/span> \u3068\u306a\u308b\u5834\u5408\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u306f\u5b9a\u6570\u95a2\u6570\u3067\u306f\u306a\u3044\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u4e0a\u3067\u9023\u7d9a\u3067\u3042\u308b\u304b\u3089\uff0c\u30ef\u30a4\u30a8\u30eb\u30b7\u30e5\u30c8\u30e9\u30b9\u306e\u5b9a\u7406\u306b\u3088\u308a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u4e0a\u3067\u7d76\u5bfe\u6700\u5927\u5024\u304a\u3088\u3073\u7d76\u5bfe\u6700\u5c0f\u5024\u3092\u53d6\u308b\u3002<\/p>\n<p>\u3055\u3089\u306b\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(a)=f(b)<\/span><\/span> \u304b\u3064 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u304c\u5b9a\u6570\u3067\u306a\u3044\u3053\u3068\u304b\u3089\uff0c\u3053\u308c\u3089\u306e\u6975\u5024\u306e\u5c11\u306a\u304f\u3068\u3082\u4e00\u3064\u306f\u5185\u90e8\u533a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u306b\u304a\u3044\u3066\u9054\u6210\u3055\u308c\u308b\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]a,b[<\/span><\/span> \u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u304c\u5c40\u6240\u7684\u6975\u5024\u3092\u53d6\u308b\u5185\u90e8\u70b9\u3068\u3059\u308b\u3068\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u4e0a\u3067\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308b\u304b\u3089\uff0c\u7279\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c)<\/span><\/span> \u304c\u5b58\u5728\u3057\uff0c\u524d\u306e\u5b9a\u7406\u3088\u308a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c)=0<\/span><\/span> \u304c\u5f93\u3046\u3002\n          <\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"4\"><\/a><\/br><\/p>\n<h2>\u5fae\u5206\u306b\u304a\u3051\u308b\u5e73\u5747\u5024\u306e\u5b9a\u7406<\/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;\">\u5148\u306b\u78ba\u8a8d\u3057\u305f\u7d50\u679c\u306e\u76f4\u63a5\u7684\u306a\u5e30\u7d50\u3068\u3057\u3066<\/span><\/strong><\/a>\uff0c\u95a2\u6570\u306e\u7814\u7a76\u306b\u6709\u7528\u306a\u60c5\u5831\u3092\u4e0e\u3048\u308b\u3082\u3046\u4e00\u3064\u306e\u7d50\u679c\u304c\uff0c\u5fae\u5206\u306b\u304a\u3051\u308b\u5e73\u5747\u5024\u306e\u5b9a\u7406\u3067\u3042\u308b\u3002\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>\u5b9a\u7406:<\/strong><\/span><br \/>\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u9023\u7d9a\u306a\u95a2\u6570\u3068\u3057\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u4e0a\u3067\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308b\u3068\u3059\u308b\u3002\u3053\u306e\u3068\u304d\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]a,b[<\/span><\/span> \u304c\u5b58\u5728\u3057\u3066\uff0c\u6b21\u304c\u6210\u308a\u7acb\u3064\u3002\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>\u8a3c\u660e:<\/strong><\/span><br \/>\n          \u6b21\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> \u3092\u8003\u3048\u308b\u3002\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          \u3053\u306e\u95a2\u6570\u306f\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u304c\u305d\u306e\u3088\u3046\u3067\u3042\u308b\u3053\u3068\u304b\u3089\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u4e0a\u3067\u9023\u7d9a\u3067\u3042\u308a\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u4e0a\u3067\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308b\u3002\u307e\u305f\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(a)=F(b)<\/span><\/span> \u304c\u6210\u308a\u7acb\u3064\u305f\u3081\uff0c\u30ed\u30eb\u306e\u5b9a\u7406\u3092\u9069\u7528\u3057\u3066\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]a,b[<\/span><\/span> \u304c\u5b58\u5728\u3057\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F^\\prime(c)=0<\/span><\/span> \u3068\u306a\u308b\u3053\u3068\u304c\u5206\u304b\u308b\u3002\n        <\/p>\n<p style=\"text-align: justify;\">\n          \u6b21\u306b\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> \u3092\u5fae\u5206\u3059\u308b\u3068\uff0c\u6b21\u3092\u5f97\u308b\u3002\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          \u3053\u308c\u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c<\/span><\/span> \u306b\u304a\u3044\u3066\u8a55\u4fa1\u3057\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F^\\prime(c)=0<\/span><\/span> \u3092\u7528\u3044\u308b\u3068\uff0c\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          \u3088\u3063\u3066\uff0c\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          \u3068\u306a\u308a\uff0c\u793a\u3059\u3079\u304d\u3053\u3068\u304c\u8a3c\u660e\u3055\u308c\u305f\u3002\n        <\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"5\"><\/a><\/br><\/p>\n<h3>\u5897\u52a0\u533a\u9593\u3068\u6e1b\u5c11\u533a\u9593<\/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>\u5b9a\u7406:<\/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;\">\u3082\u3057 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u304c\u95a2\u6570\u3067\u3042\u308a<\/span><\/strong><\/a>\uff0c<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> \u304c\u6210\u308a\u7acb\u3064\u306a\u3089\u3070\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u306b\u304a\u3044\u3066\u53b3\u5bc6\u306b\u5897\u52a0\u3059\u308b\u3002\n          <\/li>\n<li>\n            \u3082\u3057 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u304c\u95a2\u6570\u3067\u3042\u308a\uff0c<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> \u304c\u6210\u308a\u7acb\u3064\u306a\u3089\u3070\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u306b\u304a\u3044\u3066\u53b3\u5bc6\u306b\u6e1b\u5c11\u3059\u308b\u3002\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>\u8a3c\u660e:<\/strong><\/span><br \/>\n          <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1,x_2\\in ]a,b[<\/span><\/span> \u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1 \\lt x_2<\/span><\/span> \u3068\u3059\u308b\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,b[<\/span><\/span> \u4e0a\u3067\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308b\u304b\u3089\uff0c\u533a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[x_1,x_2]\\subset ]a,b[<\/span><\/span> \u306b\u304a\u3044\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u306b\u5e73\u5747\u5024\u306e\u5b9a\u7406\u3092\u9069\u7528\u3067\u304d\u308b\u3002\u3057\u305f\u304c\u3063\u3066\uff0c\u3042\u308b\u70b9 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c\\in]x_1,x_2[<\/span><\/span> \u304c\u5b58\u5728\u3057\u3066\uff0c\u6b21\u304c\u6210\u308a\u7acb\u3064\u3002\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          \u3053\u3053\u304b\u3089\u6b21\u304c\u5f93\u3046\u3002\n        <\/p>\n<ul style=\"text-align: justify;\">\n<li>\n            <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c) \\gt 0<\/span><\/span> \u306a\u3089\u3070\uff0c<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> \u3067\u3042\u308b\u3002<br \/>\n\u3057\u305f\u304c\u3063\u3066\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u306f\u5897\u52a0\u95a2\u6570\u3067\u3042\u308b\u3002\n          <\/li>\n<li>\n            <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^\\prime(c) \\lt 0<\/span><\/span> \u306a\u3089\u3070\uff0c<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> \u3067\u3042\u308b\u3002<br \/>\n\u3057\u305f\u304c\u3063\u3066\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u306f\u6e1b\u5c11\u95a2\u6570\u3067\u3042\u308b\u3002\n          <\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\n\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u3092\u5b66\u3076\u3053\u3068\u306f\uff0c\u5358\u306b\u300c\u5fae\u5206\u3092\u8a08\u7b97\u3059\u308b\u300d\u3053\u3068\u3067\u306f\u306a\u304f\uff0c\u66d6\u6627\u306a\u63a2\u7d22\u3092\uff0c\u4fdd\u8a3c\u3068\u660e\u78ba\u306a\u5224\u5b9a\u57fa\u6e96\u3092\u5099\u3048\u305f\u624b\u7d9a\u304d\u3078\u3068\u5909\u63db\u3059\u308b\u65b9\u6cd5\u3092\u8eab\u306b\u4ed8\u3051\u308b\u3053\u3068\u3067\u3042\u308b\u3002\u30ef\u30a4\u30a8\u30eb\u30b7\u30e5\u30c8\u30e9\u30b9\u306f\uff0c\u30b3\u30f3\u30d1\u30af\u30c8\u533a\u9593\u306b\u304a\u3044\u3066\u6700\u9069\u89e3\u306e\u5b58\u5728\u3092\u4fe1\u983c\u3067\u304d\u308b\u6761\u4ef6\u3092\u793a\u3057\uff0c\u4e00\u65b9\u3067\u4e00\u6b21\u5c0e\u95a2\u6570\u306e\u5224\u5b9a\u57fa\u6e96\uff0c\u30ed\u30eb\u306e\u5b9a\u7406\uff0c\u304a\u3088\u3073\u5e73\u5747\u5024\u306e\u5b9a\u7406\u306f\uff0c\u5019\u88dc\u70b9\u3092\u898b\u3064\u3051\u7d50\u8ad6\u3092\u6b63\u5f53\u5316\u3059\u308b\u305f\u3081\u306e\u9053\u7b4b\u3092\u4e0e\u3048\u308b\u3002\u3059\u306a\u308f\u3061\uff0c\u95a2\u6570\u304c\u3069\u3053\u3067\u6975\u5024\u3092\u53d6\u308a\u5f97\u308b\u306e\u304b\uff0c\u305d\u306e\u6761\u4ef6\u304c\u3044\u3064\u5fc5\u8981\u6761\u4ef6\u306b\u3068\u3069\u307e\u308b\u306e\u304b\uff0c\u305d\u3057\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f&#039;<\/span><\/span> 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