{"id":44,"date":"2023-09-17T10:56:06","date_gmt":"2023-09-17T10:56:06","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e6%9b%b2%e7%8e%87%e7%9a%84%e5%87%b9%e5%87%b8%e5%87%bd%e6%95%b0\/"},"modified":"2023-09-17T10:56:06","modified_gmt":"2023-09-17T10:56:06","slug":"%e6%9b%b2%e7%8e%87%e7%9a%84%e5%87%b9%e5%87%b8%e5%87%bd%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e6%9b%b2%e7%8e%87%e7%9a%84%e5%87%b9%e5%87%b8%e5%87%bd%e6%95%b0\/","title":{"rendered":"\u51fd\u6570\u7684\u51f9\u51f8\uff08\u66f2\u7387\uff09"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u51fd\u6570\u7684\u51f9\u6027\u548c\u51f8\u6027\uff0c\u4ee5\u53ca\u5982\u4f55\u5224\u65ad\u51fd\u6570\u662f\u51f9\u51fd\u6570\u8fd8\u662f\u51f8\u51fd\u6570\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u9010\u6b65\u7ec3\u4e60\u51fd\u6570\u66f2\u7387\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-concavidad-y-la-convexidad-de-una-funcion\"><\/span>\u4ec0\u4e48\u662f\u51fd\u6570\u7684\u51f9\u6027\u548c\u51f8\u6027\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u51fd\u6570\u7684\u51f9\u6027\u548c\u51f8\u6027\u662f\u6307\u51fd\u6570\u56fe\u5f62\u7684\u66f2\u7387\u3002<\/strong><strong>\u51f9\u51fd\u6570<\/strong>\u662f\u56fe\u5f62\u5177\u6709\u5c71\u5f62\u72b6\u7684\u51fd\u6570\uff0c<strong>\u51f8\u51fd\u6570<\/strong>\u662f\u56fe\u5f62\u5177\u6709\u5c71\u8c37\u5f62\u72b6\u7684\u51fd\u6570\u3002<\/p>\n<p>\u4e0a\u4e00\u6bb5\u4e3a\u4e86\u4fbf\u4e8e\u7406\u89e3\uff0c\u5bf9\u51f9\u51fd\u6570\u548c\u51f8\u51fd\u6570\u8fdb\u884c\u4e86\u975e\u6b63\u5f0f\u7684\u5b9a\u4e49\uff0c\u4f46\u51f9\u51fd\u6570\u548c\u51f8\u51fd\u6570\u7684\u6570\u5b66\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n<ul>\n<li><strong>\u51f9\u51fd\u6570\uff1a<\/strong>\u5f53\u51fd\u6570\u4efb\u610f\u4e24\u70b9\u76f8\u8fde\u7684\u7ebf\u6bb5\u5728\u66f2\u7ebf\u4e0b\u65b9\u65f6\u3002<\/li>\n<li><strong>\u51f8\u51fd\u6570\uff1a<\/strong>\u5f53\u51fd\u6570\u4efb\u610f\u4e24\u70b9\u76f8\u8fde\u7684\u7ebf\u6bb5\u4f4d\u4e8e\u66f2\u7ebf\u4e0a\u65b9\u65f6\u3002 <\/li>\n<\/ul>\n<div class=\"wp-block-columns is-layout-flex wp-container-9\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/fonction-concave.webp\" alt=\"\u51f9\u51fd\u6570\" class=\"wp-image-2556\" width=\"292\" height=\"300\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/fonction-convexe.webp\" alt=\"\u51f8\u51fd\u6570\" class=\"wp-image-2557\" width=\"288\" height=\"300\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<p>\u6700\u7ec8\uff0c\u51f9\u51fd\u6570\u548c\u51f8\u51fd\u6570\u4e4b\u95f4\u7684\u533a\u522b\u5728\u4e8e\u51fd\u6570\u7684\u5f62\u72b6\uff0c\u56e0\u6b64\uff0c\u60a8\u53ef\u4ee5\u4ece\u51fd\u6570\u7684\u56fe\u5f62\u4e2d\u533a\u5206\u51f9\u51fd\u6570\u548c\u51f8\u51fd\u6570\u3002<\/p>\n<p>\u7136\u800c\uff0c\u51fd\u6570\u4e0d\u4e00\u5b9a\u5728\u5176\u6574\u4e2a\u57df\u4e0a\u662f\u51f9\u51fd\u6570\u6216\u51f8\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u5728\u4e00\u4e2a\u533a\u95f4\u4e0a\u662f\u51f9\u51fd\u6570\uff0c\u5728\u53e6\u4e00\u4e2a\u533a\u95f4\u4e0a\u662f\u51f8\u51fd\u6570\u3002<\/p>\n<p class=\"has-background\" style=\"background-color:#fffde7\"><strong>\u6ce8\u610f\uff1a<\/strong>\u6570\u5b66\u754c\u4ecd\u7136\u6ca1\u6709\u5b8c\u5168\u540c\u610f\uff0c\u56e0\u6b64\uff0c\u4e00\u4e9b\u6559\u6388\u63d0\u51fa\u4e86\u76f8\u53cd\u7684\u8bf4\u6cd5\uff1a\u4ed6\u4eec\u5c06\u5f62\u72b6\u4e3a a \u7684\u51fd\u6570\u79f0\u4e3a\u51f9\u51fd\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f5ebc563dbe58138d1de6b7fe99e8d31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\cup}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\uff0c\u4ee5\u53ca\u4e00\u4e2a\u51f8\u51fd\u6570\uff0c\u5176\u5f62\u5f0f\u4e3a<strong> <\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dccbfcebef91876585ebd365457c3d24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\cap}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u3002\u65e0\u8bba\u5982\u4f55\uff0c\u91cd\u8981\u7684\u662f\u77e5\u9053\u51fd\u6570\u662f\u4ec0\u4e48\uff0c\u65e0\u8bba\u540d\u79f0\u5982\u4f55\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-estudiar-la-curvatura-de-una-funcion\"><\/span>\u5982\u4f55\u7814\u7a76\u51fd\u6570\u7684\u66f2\u7387<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7814\u7a76\u51fd\u6570\u7684\u66f2\u7387\u6d89\u53ca\u6c42\u51fd\u6570\u7684\u51f9\u51f8\u6027\uff0c\u5373\u77e5\u9053\u51fd\u6570\u51f9\u7684\u533a\u95f4\u548c\u51f8\u51fd\u6570\u7684\u533a\u95f4\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u8981\u7814\u7a76\u51fd\u6570\u7684\u66f2\u7387\uff0c\u5fc5\u987b\u6267\u884c\u4ee5\u4e0b\u6b65\u9aa4\uff1a <\/p>\n<div style=\"background-color:#FFF3E0; padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 10px; border-radius:30px;\">\n<ol style=\"color:#64B5F6; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u627e\u51fa<strong>\u4e0d\u5c5e\u4e8e\u51fd\u6570\u5b9a\u4e49\u57df\u7684\u70b9<\/strong>\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u8ba1\u7b97<strong>\u51fd\u6570\u7684\u4e00\u9636\u5bfc\u6570\u548c\u4e8c\u9636\u5bfc\u6570\u3002<\/strong><\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u6c42<strong>\u4e8c\u9636\u5bfc\u6570\u7684\u6839<\/strong>\uff0c\u5373\u901a\u8fc7\u6c42\u89e3\u8ba1\u7b97\u62b5\u6d88\u4e8c\u9636\u5bfc\u6570\u7684\u70b9\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-981d85a257dd56afdb3fc7eb53d5eadf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span>\u3002<\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u7528\u5bfc\u6570\u7684\u6839\u548c\u4e0d\u5c5e\u4e8e\u51fd\u6570\u5b9a\u4e49\u57df\u7684\u70b9\u5efa\u7acb<strong>\u533a\u95f4<\/strong>\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u8ba1\u7b97\u6bcf\u4e2a\u533a\u95f4\u4e2d\u67d0\u4e2a\u70b9\u7684\u4e8c\u9636\u5bfc\u6570\u503c\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u56e0\u6b64\uff0c<strong>\u4e8c\u9636\u5bfc\u6570\u7684\u7b26\u53f7<\/strong>\u51b3\u5b9a\u4e86\u8be5\u533a\u95f4\u5185\u51fd\u6570\u7684\u51f9\u6027\u6216\u51f8\u6027\uff1a<\/span>\n<ul style=\"color:#64B5F6; font-weight: bold; margin-top:8px; margin-left:8%\">\n<li style=\"margin-bottom:8px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u51fd\u6570\u7684\u4e8c\u9636\u5bfc\u6570\u4e3a\u6b63\uff0c\u5219\u51fd\u6570\u5728\u6b64\u533a\u95f4\u4e0a\u662f<strong>\u51f8\u51fd\u6570<\/strong>\u3002<\/span><\/li>\n<li style=\"margin-bottom:8px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u51fd\u6570\u7684\u4e8c\u9636\u5bfc\u6570\u4e3a\u8d1f\uff0c\u5219\u51fd\u6570\u5728\u6b64\u533a\u95f4\u4e0a\u662f<strong>\u51f9\u51fd\u6570<\/strong>\u3002<\/span> <\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-hallar-la-curvatura-de-una-funcion\"><\/span>\u5982\u4f55\u6c42\u51fd\u6570\u66f2\u7387\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u9010\u6b65\u6c42\u89e3\u4e00\u4e2a\u793a\u4f8b\uff0c\u4ee5\u4fbf\u60a8\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u51fd\u6570\u7684\u51f9\u51f8\u533a\u95f4\u3002<\/p>\n<ul>\n<li>\u7814\u7a76\u4ee5\u4e0b\u51fd\u6570\u7684\u51f9\u51f8\u6027\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1d76dfe92202a4fa44057a7f4576c97a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-3x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"117\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u9996\u5148\u8981\u505a\u7684\u662f\u8ba1\u7b97\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u591a\u9879\u5f0f\u51fd\u6570\uff0c\u56e0\u6b64\u51fd\u6570\u7684\u57df\u7531\u5b9e\u6570\u7ec4\u6210\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f565027fd5d2a4381e3a23d183c9f76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f= \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u8ba1\u7b97\u4e86\u51fd\u6570\u7684\u57df\uff0c\u6211\u4eec\u5c31\u9700\u8981\u7814\u7a76\u51fd\u6570\u7684\u4e8c\u9636\u5bfc\u6570\u5728\u54ea\u4e9b\u70b9\u6d88\u5931\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u8ba1\u7b97\u51fd\u6570\u7684\u4e00\u9636\u5bfc\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5e356b083f137690f09e2af3c62b8b07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-3x \\ \\longrightarrow \\ f'(x)= 3x^2-3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"287\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u7136\u540e\u6211\u4eec\u6c42\u51fd\u6570\u7684\u4e8c\u9636\u5bfc\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-016a210c39feb9d6df8caddacdbac681_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=3x^2-3 \\ \\longrightarrow \\ f''(x)= 6x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"256\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5c06\u4e8c\u9636\u5bfc\u6570\u8bbe\u7f6e\u4e3a 0 \u5e76\u6c42\u89e3\u65b9\u7a0b\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-981d85a257dd56afdb3fc7eb53d5eadf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7878c5d5f08c25729d37b94ea643bdf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-108341259f39e597d1e8c926a80dbae6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{0}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"45\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u8ba1\u7b97\u4e86\u51fd\u6570\u7684\u57df\u5e76\u4e14<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-981d85a257dd56afdb3fc7eb53d5eadf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<p>\uff0c\u6211\u4eec\u4ee3\u8868\u7ebf\u4e0a\u627e\u5230\u7684\u6240\u6709\u5173\u952e\u70b9\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5728\u8ba1\u7b97\u51fd\u6570\u5b9a\u4e49\u57df\u65f6\u6ca1\u6709\u627e\u5230\u4efb\u4f55\u4e34\u754c\u70b9\uff0c\u4f46\u6211\u4eec\u5f97\u5230\u4e86\u4e00\u4e2a\u62b5\u6d88\u51fd\u6570\u4e8c\u9636\u5bfc\u6570\u7684\u70b9\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-ligne-0.webp\" alt=\"\" class=\"wp-image-2426\" width=\"201\" height=\"77\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u73b0\u5728\u6211\u4eec\u8bc4\u4f30\u6bcf\u4e2a\u533a\u95f4\u5185\u7684\u4e8c\u9636\u5bfc\u6570\u7684\u7b26\u53f7\uff0c\u4ee5\u4e86\u89e3\u8be5\u51fd\u6570\u662f\u51f9\u51fd\u6570\u8fd8\u662f\u51f8\u51fd\u6570\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5728\u6bcf\u4e2a\u533a\u95f4\u53d6\u4e00\u4e2a\u70b9\uff08\u800c\u4e0d\u662f\u4e34\u754c\u70b9\uff09\uff0c\u5e76\u67e5\u770b\u6b64\u65f6\u4e8c\u9636\u5bfc\u6570\u7684\u7b26\u53f7\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-86d5e98dcde33659284eaafb55050852_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=6x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ab7d8a0d32ae8b29c211f51359c61a4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(-1) = 6\\cdot (-1)=-6 \\  \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"236\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-084869779374d781df1af76f0aa784ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(1) = 6\\cdot 1=+6 \\  \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/droite-numerique-0-concave-convexe.webp\" alt=\"\" class=\"wp-image-2561\" width=\"201\" height=\"134\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u63a8\u5bfc\u51fa\u51fd\u6570\u7684\u51f9\u51f8\u533a\u95f4\u3002\u5982\u679c\u4e8c\u9636\u5bfc\u6570\u4e3a\u6b63\uff0c\u5219\u8868\u793a\u8be5\u51fd\u6570\u662f\u51f8\u51fd\u6570\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> \uff0c\u5982\u679c\u4e8c\u9636\u5bfc\u6570\u4e3a\u8d1f\uff0c\u5219\u610f\u5473\u7740\u8be5\u51fd\u6570\u662f\u51f9\u51fd\u6570<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u3002\u56e0\u6b64\u51fd\u6570\u7684\u51f9\u51f8\u533a\u95f4\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u51f8\u9762<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p><strong>:<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91ffae1f3397d9d66e3159e131554abb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(0,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u51f9<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p><strong>:<\/strong> <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bec51dbadb80b73308bcb5a625cd152f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,0)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-concavidad-y-convexidad-de-una-funcion\"><\/span>\u89e3\u51b3\u4e86\u51fd\u6570\u7684\u51f9\u6027\u548c\u51f8\u6027\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u591a\u9879\u5f0f\u51fd\u6570\u7684\u51f9\u51f8\u533a\u95f4\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9cd1ae6bdb4d8dbd44ef2561f6e022fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = x^3-3x^2-2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"165\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u7ec3\u4e60\u4e2d\u7684\u51fd\u6570\u662f\u591a\u9879\u5f0f\uff0c\u56e0\u6b64\u51fd\u6570\u7684\u57df\u7531\u5b9e\u6570\u7ec4\u6210\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f565027fd5d2a4381e3a23d183c9f76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f= \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u786e\u5b9a\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u540e\uff0c\u6211\u4eec\u5bf9\u5176\u8fdb\u884c\u5fae\u5206\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0a14436352ca08e03441a24b9e881093_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-3x^2-2x \\ \\longrightarrow \\  f'(x)= 3x^2-6x-2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"375\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7136\u540e\u6211\u4eec\u6c42\u51fd\u6570\u7684\u4e8c\u9636\u5bfc\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8ec8542448a8f4aa326a2d70f5f5efb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)= 3x^2-6x-2 \\ \\longrightarrow \\ f''(x)= 6x-6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"327\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06\u4e8c\u9636\u5bfc\u6570\u8bbe\u7f6e\u4e3a 0 \u5e76\u6c42\u89e3\u65b9\u7a0b\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f618f4961c18c45be60fc496ad4896e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c644c35f109a535e50e1bda440f12db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x-6= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7b7a2a9a8deaab9c4eb4761838f99407_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x= 6\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8ddd3a5381ed7b33d4e9dfbc270c1da3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= \\cfrac{6}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"45\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3330a01aa4d7d81947b71297d8623d3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u8ba1\u7b97\u4e86\u51fd\u6570\u7684\u57df\u5e76\u6c42\u89e3<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-981d85a257dd56afdb3fc7eb53d5eadf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<p>\uff0c\u6211\u4eec\u8868\u793a\u6570\u8f74\u4e0a\u627e\u5230\u7684\u6240\u6709\u5947\u5f02\u70b9\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-ligne-1.webp\" alt=\"\" class=\"wp-image-2564\" width=\"213\" height=\"83\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u73b0\u5728\u8ba9\u6211\u4eec\u53d6\u4e00\u4e2a\u5c5e\u4e8e\u6bcf\u4e2a\u533a\u95f4\u7684\u70b9\uff0c\u770b\u770b\u6b64\u65f6\u7684\u4e8c\u9636\u5bfc\u6570\u662f\u4ec0\u4e48\u7b26\u53f7\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4e4f2f534e4134661dfda2b6b8125ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(0)= 6\\cdot 0-6 = -6 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"225\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59d344f0c0b93695edf55652112bf6e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(2)= 6\\cdot 2-6 = 12-6=+6 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"297\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/droite-numerique-1-concave-convexe.webp\" alt=\"\" class=\"wp-image-2565\" width=\"224\" height=\"150\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u5f53\u4e8c\u9636\u5bfc\u6570\u5927\u4e8e\u96f6\u65f6\uff0c\u8868\u793a\u51fd\u6570\u662f\u51f8\u51fd\u6570\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> \uff0c\u4f46\u662f\u5f53\u4e8c\u9636\u5bfc\u6570\u4e3a\u8d1f\u65f6\uff0c\u8fd9\u610f\u5473\u7740\u8be5\u51fd\u6570\u662f\u51f9\u51fd\u6570<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u3002\u56e0\u6b64\uff0c\u51f9\u51f8\u533a\u95f4\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u51f8\u9762<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p><strong>:<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-87d6843b66a0ebea6c769017a30a8d75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(1,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u51f9<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p><strong>:<\/strong> <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-36b85798b30f125fea3702a0671c77ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u7814\u7a76\u4ee5\u4e0b\u6709\u7406\u51fd\u6570\u7684\u66f2\u7387\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3ac9ccc5e8540cca38f599ed36507792_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{x^3}{x^2-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"109\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u9996\u5148\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u51fd\u6570\u7684\u57df\u3002\u7531\u4e8e\u8fd9\u662f\u4e00\u4e2a\u6709\u7406\u51fd\u6570\uff0c\u6211\u4eec\u5c06\u5206\u6bcd\u8bbe\u7f6e\u4e3a\u96f6\uff0c\u770b\u770b\u54ea\u4e9b\u6570\u5b57\u4e0d\u5c5e\u4e8e\u51fd\u6570\u7684\u57df\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a34dfe78d673534873a2013c16e1b353_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-4= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"81\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c269e23a1070b3e5556abece040af75a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2=4\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c4c32359b264b28ac80f2606c09d5a2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{x^2}=\\sqrt{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c06a55e3acdd1e283973786926b27716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\pm 2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8fd9\u610f\u5473\u7740\u5f53x\u4e3a-2\u6216+2\u65f6\uff0c\u5206\u6bcd\u5c06\u4e3a0\u3002\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u5c06\u4e0d\u5b58\u5728\u3002\u56e0\u6b64\uff0c\u51fd\u6570\u7684\u57df\u7531\u9664 x=-2 \u548c x=+2 \u4e4b\u5916\u7684\u6240\u6709\u6570\u5b57\u7ec4\u6210\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e666f828709575f965b5120fbdda085e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f= \\mathbb{R}-\\{-2, +2 \\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"182\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5176\u6b21\uff0c\u6211\u4eec\u8ba1\u7b97\u51fd\u6570\u7684\u4e00\u9636\u5bfc\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1397d0e8e73bd7b1d851411dee28daed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x^3}{x^2-4}  \\ \\longrightarrow \\ f'(x)= \\cfrac{3x^2 \\cdot (x^2-4) - x^3 \\cdot 2x }{\\left(x^2-4\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"396\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-495f08a881718b2734ef1db17b5f39ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)= \\cfrac{3x^4-12x^2-2x^4}{\\left(x^2-4\\right)^2} = \\cfrac{x^4-12x^2}{\\left(x^2-4\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"298\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7136\u540e\u6211\u4eec\u6c42\u89e3\u4e8c\u9636\u5bfc\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-50df15bb48cacf8f031b640994661e47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{\\left(4x^3-24x\\right)\\cdot \\left(x^2-4\\right)^2 - \\left(x^4-12x^2\\right)\\cdot 2\\left(x^2-4\\right)\\cdot 2x }{ \\left(\\left(x^2-4\\right)^2 \\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"483\" style=\"vertical-align: -33px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b05b5f09c2adbfead593df2cdf2ad29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{\\left(4x^3-24x\\right)\\cdot \\left(x^2-4\\right)^2 - \\left(x^4-12x^2\\right)\\cdot 4x\\left(x^2-4\\right) }{\\left(x^2-4\\right)^4 }\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"461\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u6709\u9879\u5747\u4e58\u4ee5<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1e0f0d9a63183e28c50a5cedcddeddd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x^2-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u3002\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u7b80\u5316\u5206\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-92e1aa280d06bf8b58045845d5e21f37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{\\left(4x^3-24x\\right)\\cdot \\left(x^2-4\\right)^{\\cancel{2}} - \\left(x^4-12x^2\\right)\\cdot 4x\\cancel{\\left(x^2-4\\right)} }{\\left(x^2-4\\right)^{\\cancelto{3}{4}} }\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"458\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a912eff3359969b6ffbef96a3f16932d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{\\left(4x^3-24x\\right)\\cdot \\left(x^2-4\\right) - \\left(x^4-12x^2\\right)\\cdot 4x}{\\left(x^2-4\\right)^3 }\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"386\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8bc35bdd2b70bbac52fa0f24bbefa261_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{4x^5-16x^3-24x^3+96x - \\left(4x^5-48x^3\\right) }{\\left(x^2-4\\right)^3 }\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"381\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-045971f71cc11ced77ea0df9f2c514fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{4x^5-16x^3-24x^3+96x - 4x^5+48x^3 }{\\left(x^2-4\\right)^3 }\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"365\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3144a0aa00ee8ec427752f05f0fac40c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{8x^3+96x  }{\\left(x^2-4\\right)^3 }\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"145\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u6765\u8ba1\u7b97\u51fd\u6570\u4e8c\u9636\u5bfc\u6570\u7684\u6839\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f618f4961c18c45be60fc496ad4896e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e8ed519add27a4d51c75b49179e632ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{8x^3+96x  }{\\left(x^2-4\\right)^3 }=0\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"109\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u671f\u9650<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8590a90fab5aef55d7b45cd89e01943_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x^2-4\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"70\" style=\"vertical-align: -7px;\"><\/p>\n<p>\u8fd9\u6d89\u53ca\u5230\u5c06\u6574\u4e2a\u5de6\u4fa7\u9664\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5c06\u5176\u4e58\u4ee5\u6574\u4e2a\u53f3\u4fa7\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b5c0d1e44accc3b68a67598f5c4d834c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^3+96x =0\\cdot \\left(x^2-4\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"193\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4c52a7448e4acc67488ef5747cc3bed9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^3+96x =0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"109\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u63d0\u53d6\u516c\u56e0\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f2884a1c9b8dabf6ea5323f2ac71b2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x(8x^2+96)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u4f7f\u4e58\u6cd5\u7b49\u4e8e 0\uff0c\u4e58\u6cd5\u7684\u4e24\u4e2a\u5143\u7d20\u4e4b\u4e00\u5fc5\u987b\u4e3a\u96f6\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u6bcf\u4e2a\u56e0\u5b50\u8bbe\u7f6e\u4e3a0\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-31adba554b44aa92fd7227506440ccaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle x\\cdot(8x^2+96) =0 \\longrightarrow \\begin{cases} \\bm{x =0} \\\\[2ex] 8x^2+96=0 \\ \\longrightarrow \\ x^2=\\cfrac{-96}{8}} = -12 \\ \\longrightarrow \\ x= \\sqrt{-12} \\ \\color{red}\\bm{\\times} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"635\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-635e2ffa452a5a66a4bcacb0e111c5ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= \\sqrt{-12}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"81\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u6ca1\u6709\u89e3\uff0c\u56e0\u4e3a\u5b9e\u6570\u6ca1\u6709\u8d1f\u6839\u3002<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5728\u7ebf\u4e0a\u8868\u793a\u6240\u6709\u83b7\u5f97\u7684\u4e34\u754c\u70b9\uff0c\u5373\u4e0d\u5c5e\u4e8e\u5b9a\u4e49\u57df\u7684\u70b9\uff08x=-2 \u548c x=+2\uff09\u4ee5\u53ca\u53d6\u6d88\u4e8c\u9636\u5bfc\u6570\u7684\u70b9\uff08x=0\uff09\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/droite-numerique-2-0-2.webp\" alt=\"\" class=\"wp-image-2399\" width=\"385\" height=\"75\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8bc4\u4f30\u6bcf\u4e2a\u533a\u95f4\u5185\u7684\u4e8c\u9636\u5bfc\u6570\u7684\u7b26\u53f7\uff0c\u4ee5\u4e86\u89e3\u8be5\u51fd\u6570\u662f\u51f9\u51fd\u6570\u8fd8\u662f\u51f8\u51fd\u6570\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5728\u6bcf\u4e2a\u533a\u95f4\u4e2d\u53d6\u4e00\u4e2a\u70b9\uff0c\u770b\u770b\u8be5\u70b9\u7684\u4e8c\u9636\u5bfc\u6570\u7684\u7b26\u53f7\u662f\u4ec0\u4e48\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b5618d1ab96a078d50507f45155595b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(-3)=\\cfrac{8(-3)^3+96(-3)  }{\\left((-3)^2-4\\right)^3 } = \\cfrac{-504}{125}=-4,03 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"408\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e2e868f1f815d4155a187c55b004cc13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(-1)=\\cfrac{8(-1)^3+96(-1)  }{\\left((-1)^2-4\\right)^3 } = \\cfrac{-104}{-27}=3,85 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"394\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3814746f7f9e8aa3920e3f84cd0ff0eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(1)=\\cfrac{8\\cdot1^3+96\\cdot 1  }{\\left(1^2-4\\right)^3 } = \\cfrac{104}{-27}=-3,85 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"348\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-54d98824f72954de12bc065471a610e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(3)=\\cfrac{8\\cdot 3^3+96\\cdot 3  }{\\left(3^2-4\\right)^3 } = \\cfrac{504}{125}=4,03 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"329\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-2-0-2-courbure.webp\" alt=\"\" class=\"wp-image-2568\" width=\"383\" height=\"129\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u5982\u679c\u4e8c\u9636\u5bfc\u6570\u4e3a\u6b63\uff0c\u5219\u8868\u793a\u8be5\u51fd\u6570\u662f\u51f8\u51fd\u6570\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> \uff0c\u5982\u679c\u4e8c\u9636\u5bfc\u6570\u4e3a\u8d1f\uff0c\u5219\u610f\u5473\u7740\u8be5\u51fd\u6570\u662f\u51f9\u51fd\u6570<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u3002\u56e0\u6b64\uff0c\u51f9\u5ea6\u548c\u51f8\u5ea6\u533a\u95f4\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u51f8\u9762<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p><strong>:<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0cd739761b2dc845594c0a0696a240c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-2,0)\\cup (2,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"134\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u51f9<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p><strong>:<\/strong> <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5e741ac026627200772655094f921f26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,-2)\\cup (0,2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u4e00\u4e2a\u529f\u80fd<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u5177\u6709\u76f8\u5bf9\u6781\u7aef\u7684<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3573bf1ea4c223bb71878796b2106731_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u3002\u66f4\u91cd\u8981\u7684\u662f\uff0c\u8be5\u51fd\u6570\u662f\u51f8\u51fd\u6570<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c5b03f70f64c85542b93152492ab8bd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\cup )\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u5728\u540c\u4e00\u70b9\u4e0a\u3002\u786e\u5b9a\u76f8\u5bf9\u6781\u503c\u662f\u6700\u5c0f\u503c\u8fd8\u662f\u6700\u5927\u503c\u3002<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u51fd\u6570\u76f8\u5bf9\u6781\u503c\u7684\u6781\u5927\u6781\u5c0f\u503c\/\">\u51fd\u6570\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u7684\u5b9a\u4e49<\/a><\/span><\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8bbe\u51f8\u51fd\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d2bb599fff4b55075f6de7628a35f822_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\cup)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u5728<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3573bf1ea4c223bb71878796b2106731_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u8868\u793a\u6b64\u65f6\u7684\u4e8c\u9636\u5bfc\u6570\u4e3a\u6b63\uff0c\u5373<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6e1c4b76e92a6fd3dd8c16dfb2ca8cf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(3)>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;19&#8243; width=&#8221;74&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<p>\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u76f8\u5bf9\u6781\u7aef<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2176aa2efb23d1fbd644eff672465ff0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=3}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<p><strong>\u8fd9\u662f\u6700\u5c0f\u503c<\/strong>\uff0c\u56e0\u4e3a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8cfc4aa0fa7cede2c69561e8b65a6991_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"41\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u8fd9\u662f\u79ef\u6781\u7684\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u51fd\u6570\u7684\u51f9\u6027\u548c\u51f8\u6027\uff0c\u4ee5\u53ca\u5982\u4f55\u5224\u65ad\u51fd\u6570\u662f\u51f9\u51fd\u6570\u8fd8\u662f\u51f8\u51fd\u6570\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u9010\u6b65\u7ec3\u4e60\u51fd\u6570\u66f2\u7387\u3002  &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e6%9b%b2%e7%8e%87%e7%9a%84%e5%87%b9%e5%87%b8%e5%87%bd%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u51fd\u6570\u7684\u51f9\u51f8\uff08\u66f2\u7387\uff09<\/span> \u67e5\u770b\u5168\u6587 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