{"id":2138,"date":"2024-06-11T15:07:32","date_gmt":"2024-06-11T07:07:32","guid":{"rendered":"https:\/\/17aitech.com\/?p=2138"},"modified":"2024-10-08T15:21:06","modified_gmt":"2024-10-08T07:21:06","slug":"%e3%80%90%e9%87%8d%e6%8b%be%e6%95%b0%e5%ad%a6%e7%9f%a5%e8%af%86%e3%80%91%e5%af%bc%e6%95%b0%e3%80%81%e6%9e%81%e5%80%bc%e5%92%8c%e6%9c%80%e5%80%bc","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=2138","title":{"rendered":"\u3010\u91cd\u62fe\u6570\u5b66\u77e5\u8bc6\u3011\u5bfc\u6570\u3001\u6781\u503c\u548c\u6700\u503c"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_78 ez-toc-wrap-left-text counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">\u6587\u7ae0\u76ee\u5f55<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/17aitech.com\/?p=2138\/#%E5%89%8D%E8%A8%80\" >\u524d\u8a00<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/17aitech.com\/?p=2138\/#%E7%9B%B8%E5%85%B3%E6%A6%82%E5%BF%B5\" >\u76f8\u5173\u6982\u5ff5<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/17aitech.com\/?p=2138\/#%E5%AF%BC%E6%95%B0\" >\u5bfc\u6570<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/17aitech.com\/?p=2138\/#%E4%B8%80%E4%B8%AA%E9%97%AE%E9%A2%98\" >\u4e00\u4e2a\u95ee\u9898<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/17aitech.com\/?p=2138\/#%E5%AE%9A%E4%B9%89\" >\u5b9a\u4e49<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/17aitech.com\/?p=2138\/#%E5%B8%B8%E8%A7%81%E6%B1%82%E5%AF%BC%E5%85%AC%E5%BC%8F\" >\u5e38\u89c1\u6c42\u5bfc\u516c\u5f0f<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/17aitech.com\/?p=2138\/#%E5%81%8F%E5%AF%BC\" >\u504f\u5bfc<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/17aitech.com\/?p=2138\/#%E5%AE%9A%E4%B9%89-2\" >\u5b9a\u4e49<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/17aitech.com\/?p=2138\/#%E6%9E%81%E5%80%BC%E4%B8%8E%E6%9C%80%E5%80%BC\" >\u6781\u503c\u4e0e\u6700\u503c<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/17aitech.com\/?p=2138\/#%E5%AE%9A%E4%B9%89-3\" >\u5b9a\u4e49<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/17aitech.com\/?p=2138\/#%E6%9E%81%E5%A4%A7%E5%80%BC%E5%92%8C%E6%9E%81%E5%B0%8F%E5%80%BC\" >\u6781\u5927\u503c\u548c\u6781\u5c0f\u503c<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/17aitech.com\/?p=2138\/#%E5%8F%82%E8%80%83%E8%B5%84%E6%96%99\" >\u53c2\u8003\u8d44\u6599<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E5%89%8D%E8%A8%80\"><\/span>\u524d\u8a00<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u6df1\u5ea6\u5b66\u4e60\u4e2d\uff0c\u68af\u5ea6\u4e0b\u964d\u6cd5\u662f\u4e00\u79cd\u5e38\u7528\u7684\u4f18\u5316\u7b97\u6cd5\uff0c\u7528\u4e8e\u66f4\u65b0\u6a21\u578b\u53c2\u6570\u4ee5\u6700\u5c0f\u5316\u635f\u5931\u51fd\u6570\u3002\u8fd9\u68af\u5ea6\u4e0b\u964d\u6cd5\u4e2d\u6d89\u53ca\u5230\u6570\u5b66\u4e2d\u7684<code>\u5bfc\u6570<\/code>\u3001<code>\u6781\u503c<\/code>\u7b49\u76f8\u5173\u77e5\u8bc6\uff0c\u56e0\u6b64\u6211\u4eec\u91cd\u65b0\u56de\u987e\u76f8\u5173\u5185\u5bb9\uff0c\u4ee5\u4fbf\u52a0\u6df1\u7406\u89e3\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E7%9B%B8%E5%85%B3%E6%A6%82%E5%BF%B5\"><\/span>\u76f8\u5173\u6982\u5ff5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"%E5%AF%BC%E6%95%B0\"><\/span>\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"%E4%B8%80%E4%B8%AA%E9%97%AE%E9%A2%98\"><\/span>\u4e00\u4e2a\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u5982\u4f55\u6c42\u5f97\u4e00\u4e2a\u66f2\u7ebff(x)\u4e2d\u4efb\u610f\u4e00\u70b9(x0)\u7684\u659c\u7387\uff1f<br \/>\n<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611140058308.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611140058308.png\" alt=\"\" \/><\/a><\/p>\n<p>\u6838\u5fc3\u601d\u60f3\uff1a\u5728\u66f2\u7ebf\u4e0a\u53e6\u5916\u5b58\u5728\u4e00\u4e2aP\u70b9\uff0cP\u70b9\u65e0\u9650\u63a5\u8fd1x0\uff0cx0\u548cP\u7684\u8fde\u7ebf\u5c06\u65e0\u9650\u63a5\u8fd1x0\u70b9\u7684\u659c\u7387\u3002<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611140559602.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611140559602.png\" alt=\"\" \/><\/a><\/p>\n<p>\u5728\u4e0a\u56fe\u4e2d\uff1a<\/p>\n<ul>\n<li>\n<p>\u6211\u4eec\u6c42x0\u70b9\u548cP\u70b9\u7684\u4e4b\u95f4\u7684\u659c\u7387\u4e3a\uff1a<\/p>\n<p>\u659c\u7387\u516c\u5f0f\uff1a<\/p>\n<p><code class=\"katex-inline\">k = \\frac{y_1-y_2}{x_1-x_2} = \\frac{f(x_0+\u0394x) - f(x_0)}{\u0394x}<\/code><\/p>\n<\/li>\n<li>\n<p>\u52a0\u5165\u6781\u9650\u6761\u4ef6\u0394x\u21920\u8d8b\u8fd1\u4e8e0\u65f6<\/p>\n<p><code class=\"katex-inline\">f'(x) = lim(\u0394x->0) \\frac{f(x + \u0394x) - f(x)}{\u0394x}<\/code><\/p>\n<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"%E5%AE%9A%E4%B9%89\"><\/span>\u5b9a\u4e49<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><code>\u5bfc\u6570<\/code>\u8868\u793a\u51fd\u6570 f(x) \u5728\u67d0\u4e00\u70b9 x \u5904\u7684\u53d8\u5316\u7387(\u6216\u659c\u7387)\uff0c\u901a\u5e38\u8bb0\u4f5c f'(x) \u6216 df\/dx\u3002<\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E5%B8%B8%E8%A7%81%E6%B1%82%E5%AF%BC%E5%85%AC%E5%BC%8F\"><\/span>\u5e38\u89c1\u6c42\u5bfc\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611143346720.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611143346720.png\" alt=\"\" \/><\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E5%81%8F%E5%AF%BC\"><\/span>\u504f\u5bfc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u63a5\u7740\uff0c\u6211\u4eec\u770b\u4e0b\u4ec0\u4e48\u662f\u504f\u5bfc\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n<ul>\n<li>\u5728\u5de6\u4fa7\u7684\u4e8c\u7ef4\u5e73\u9762\u4e2d\uff0c\u4e00\u5143\u51fd\u6570f(x)\u5728x0\u7684\u5bfc\u6570\u4e3ax0\u70b9\u7684\u659c\u7387\uff0c\u5373\u4e3a\u5bfc\u6570\uff1b<\/li>\n<li>\u5728\u53f3\u4fa7\u7684\u4e09\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u4e8c\u5143\u51fd\u6570z = f(x,y)\uff0c\u5728<strong>\u56fa\u5b9a\u4f4fy\u5750\u6807\u8f74<\/strong>(\u5373\uff1ay=y0\uff0c\u5982\u56fe\u4e2d\u9ed1\u8272\u7ebf\u6bb5\u5411\u4e0b\u5207\u6240\u793a)\u65f6\uff0c\u6c42z=f(x, y0)\u5728x0\u7684\u5bfc\u6570\uff0c\u5373\u4e3a<code>\u504f\u5bfc\u6570<\/code>\u3002<\/li>\n<\/ul>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611142839233.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611142839233.png\" alt=\"\" \/><\/a><\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E5%AE%9A%E4%B9%89-2\"><\/span>\u5b9a\u4e49<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>\n<p><strong>\u504f\u5bfc\u6570<\/strong>\u662f\u591a\u5143\u51fd\u6570\u5728\u67d0\u4e00\u70b9\u4e0a\u5bf9\u67d0\u4e2a\u7279\u5b9a\u53d8\u91cf\u7684\u5bfc\u6570\uff0c\u5373\u51fd\u6570\u5728\u8be5\u70b9\u4e0a\u6cbf\u7740\u67d0\u4e2a\u5750\u6807\u8f74\u65b9\u5411\u7684\u53d8\u5316\u7387\u3002<\/p>\n<blockquote>\n<p>\u504f\u5bfc\u6570\u672c\u8d28\u4e0a\u662f\u5728\u591a\u5143\u51fd\u6570\u4e2d\uff0c\u901a\u8fc7\u56fa\u5b9a\u67d0\u4e00\u53d8\u91cf\u4e3a\u5e38\u91cf\uff0c\u5c06\u591a\u5143\u964d\u7ef4\u3002<\/p>\n<\/blockquote>\n<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"%E6%9E%81%E5%80%BC%E4%B8%8E%E6%9C%80%E5%80%BC\"><\/span>\u6781\u503c\u4e0e\u6700\u503c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5728\u4e0b\u9762\u56fe\u4f8b\u51fd\u6570\u4e2d\uff0c<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611144039485.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611144039485.png\" alt=\"\" \/><\/a><\/p>\n<p><code class=\"katex-inline\">f(x) = \\frac{1}{3}x^3 + \\frac{1}{2}x^2 - 2x - 1<\/code><\/p>\n<p>\u901a\u8fc7\u6c42\u5bfc\uff0c\u5f97\u5230\u5bfc\u6570\u4e3a<\/p>\n<p><code class=\"katex-inline\">f'(x)  = x^2 + x -2<\/code><\/p>\n<p>\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li>\n<p>\u89e3\u65b9\u7a0bf'(x) = 0\uff0c\u5f97\u5230\u6781\u503c\u70b9\u4e3a x = -2 \u548c x = 1<\/p>\n<ul>\n<li>\n<p>\u5f53x = -2\u65f6\uff0cf'(x) &lt; 0\uff1b<\/p>\n<\/li>\n<li>\n<p>\u5f53x = 1 \u65f6\uff0cf'(x) &gt; 0\uff1b<\/p>\n<\/li>\n<li>\n<p>\u4e5f\u5c31\u662f\u8bf4\uff1ax=-2\u7684\u5de6\u4fa7\u662f<code>\u5355\u8c03\u9012\u589e<\/code>\uff0cx=-2\u5230x=1\u4e4b\u95f4\u662f<code>\u5355\u8c03\u9012\u51cf<\/code>\uff0cx=-2\u8fd9\u4e2a\u70b9\u6bd4\u5de6\u8fb9<strong>\u8981\u9ad8<\/strong>\uff0c\u6bd4\u53f3\u4fa7\u4e5f\u8981\u9ad8\uff0c\u6211\u4eec\u628a\u8fd9\u79cd\u70b9\u6210\u4e3a\u6781\u503c\u70b9\u3002<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"%E5%AE%9A%E4%B9%89-3\"><\/span>\u5b9a\u4e49<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>\n<p><strong>\u6781\u503c<\/strong>\u662f\u51fd\u6570\u5728\u67d0\u4e00\u70b9\u6216\u67d0\u4e00\u533a\u95f4\u5185\u53d6\u5f97\u7684\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\u3002\u6781\u5927\u503c\u662f\u51fd\u6570\u5728\u8be5\u70b9\u9644\u8fd1\u53d6\u5f97\u7684\u6700\u5927\u503c\uff0c\u6781\u5c0f\u503c\u662f\u51fd\u6570\u5728\u8be5\u70b9\u9644\u8fd1\u53d6\u5f97\u7684\u6700\u5c0f\u503c\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u6700\u503c<\/strong>\u662f\u51fd\u6570\u5728\u5b9a\u4e49\u57df\u5185\u53d6\u5f97\u7684\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\u3002\u6700\u5927\u503c\u662f\u51fd\u6570\u5728\u6574\u4e2a\u5b9a\u4e49\u57df\u5185\u53d6\u5f97\u7684\u6700\u5927\u503c\uff0c\u6700\u5c0f\u503c\u662f\u51fd\u6570\u5728\u6574\u4e2a\u5b9a\u4e49\u57df\u5185\u53d6\u5f97\u7684\u6700\u5c0f\u503c\u3002<\/p>\n<\/li>\n<\/ul>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611144654615.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611144654615.png\" alt=\"\" \/><\/a><\/p>\n<blockquote>\n<p>\u7279\u522b\u6ce8\u610f\uff1a\u6781\u503c\u2260\u6700\u503c\uff1b\u4e00\u4e2a\u66f2\u7ebf\u5728\u4e00\u6bb5\u533a\u95f4\u5185\uff0c\u53ef\u80fd\u6709\u591a\u4e2a\u6781\u503c\uff0c\u4f46\u6700\u503c\u53ea\u6709\u4e00\u4e2a\u3002<\/p>\n<\/blockquote>\n<h4><span class=\"ez-toc-section\" id=\"%E6%9E%81%E5%A4%A7%E5%80%BC%E5%92%8C%E6%9E%81%E5%B0%8F%E5%80%BC\"><\/span>\u6781\u5927\u503c\u548c\u6781\u5c0f\u503c<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u82e5x0\u662f\u6781\u503c\u70b9\uff0c\u5219f'(x0) = 0\uff0c\u8fd9\u79cd\u60c5\u51b5\u4e0b\u6709\u4e24\u79cd\u53ef\u80fd\uff1a<\/p>\n<ul>\n<li>\u82e5\u5bfc\u51fd\u6570\u7531\u6b63\u5f80\u8d1f\uff0c\u90a3\u4e48\u5bf9\u5e94\u539f\u51fd\u6570\u5148\u589e\u540e\u51cf\uff0c\u90a3\u4e48x0\u4e3a\u6781\u5927\u503c\u70b9\u3002<\/li>\n<li>\u82e5\u5bfc\u51fd\u6570\u7531\u8d1f\u5f80\u6b63\uff0c\u90a3\u4e48\u5bf9\u5e94\u539f\u51fd\u6570\u5148\u51cf\u540e\u589e\uff0c\u90a3\u4e48x0\u4e3a\u6781\u5c0f\u503c\u70b9\u3002<\/li>\n<\/ul>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611145219979.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240611145219979.png\" alt=\"\" \/><\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E5%8F%82%E8%80%83%E8%B5%84%E6%96%99\"><\/span>\u53c2\u8003\u8d44\u6599<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a 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