{"id":43,"date":"2023-09-17T10:56:20","date_gmt":"2023-09-17T10:56:20","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%87%bd%e6%95%b0%e7%9b%b8%e5%af%b9%e6%9e%81%e5%80%bc%e7%9a%84%e6%9e%81%e5%a4%a7%e6%9e%81%e5%b0%8f%e5%80%bc\/"},"modified":"2023-09-17T10:56:20","modified_gmt":"2023-09-17T10:56:20","slug":"%e5%87%bd%e6%95%b0%e7%9b%b8%e5%af%b9%e6%9e%81%e5%80%bc%e7%9a%84%e6%9e%81%e5%a4%a7%e6%9e%81%e5%b0%8f%e5%80%bc","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%87%bd%e6%95%b0%e7%9b%b8%e5%af%b9%e6%9e%81%e5%80%bc%e7%9a%84%e6%9e%81%e5%a4%a7%e6%9e%81%e5%b0%8f%e5%80%bc\/","title":{"rendered":"\u51fd\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\uff08\u76f8\u5bf9\u6781\u503c\uff09"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u51fd\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u4e24\u4e2a\u793a\u4f8b\u6765\u5411\u60a8\u89e3\u91ca\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u9010\u6b65\u7ec3\u4e60\u51fd\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-maximos-y-minimos-de-una-funcion\"><\/span>\u51fd\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u662f\u591a\u5c11\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u51fd\u6570\u7684\u6700\u5927\u503c\u662f\u51fd\u6570\u7684\u6700\u5927\u503c\uff0c\u51fd\u6570\u7684\u6700\u5c0f\u503c\u662f\u51fd\u6570\u7684\u6700\u5c0f\u503c\u3002<\/strong>\u5f53\u51fd\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u4ec5\u8868\u793a\u5176\u73af\u5883\u4e2d\u7684\u6700\u5927\u6216\u6700\u5c0f\u503c\u65f6\uff0c\u5b83\u4eec\u662f<strong>\u76f8\u5bf9\u6781\u503c<\/strong>\uff0c\u4f46\u5f53\u5b83\u4eec\u8868\u793a\u6574\u4e2a\u51fd\u6570\u7684\u6700\u5927\u6216\u6700\u5c0f\u503c\u65f6\uff0c\u5b83\u4eec\u662f<strong>\u7edd\u5bf9\u6781\u503c<\/strong>\u3002 <\/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\/maximums-et-minimums-d-une-fonction.webp\" alt=\"\u51fd\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\" class=\"wp-image-2437\" width=\"512\" height=\"420\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u60a8\u8fd8\u53ef\u4ee5\u901a\u8fc7\u7814\u7a76<strong>\u51fd\u6570\u7684\u589e\u957f\u548c\u4e0b\u964d<\/strong>\u6765\u8bc6\u522b\u76f8\u5bf9\u6781\u503c\uff1a<\/p>\n<ul>\n<li>\u70b9\u662f\u51fd\u6570\u4ece\u589e\u52a0\u5230\u51cf\u5c11\u65f6\u7684<strong>\u76f8\u5bf9\u6700\u5927\u503c<\/strong>\u3002<\/li>\n<li>\u5f53\u51fd\u6570\u4ece\u51cf\u5c11\u5230\u589e\u52a0\u65f6\uff0c\u70b9\u662f<strong>\u76f8\u5bf9\u6700\u5c0f\u503c<\/strong>\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-hallar-los-maximos-y-minimos-de-una-funcion\"><\/span>\u5982\u4f55\u6c42\u51fd\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6839\u636e\u51fd\u6570\u7684\u4e00\u9636\u5bfc\u6570\u548c\u4e8c\u9636\u5bfc\u6570\uff0c\u6211\u4eec\u53ef\u4ee5\u77e5\u9053\u51fd\u6570\u5728\u67d0\u70b9\u662f\u5426\u5b58\u5728\u76f8\u5bf9\u6781\u503c\uff0c\u4ee5\u53ca\u8be5\u70b9\u662f\u76f8\u5bf9\u6700\u5927\u503c\u8fd8\u662f\u76f8\u5bf9\u6700\u5c0f\u503c\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<ul style=\"color:#64B5F6; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u51fd\u6570\u5177\u6709<strong>\u76f8\u5bf9\u4e8e\u62b5\u6d88\u5176\u4e00\u9636\u5bfc\u6570\u7684\u70b9\u7684\u6781\u503c<\/strong>\u3002<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d6dcc4b4bb7f26cf48a025c8e0dddf83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(a)=0 \\quad \\bm{\\longrightarrow} \\quad x=a \\text{ es un extremo relativo}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"357\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u51fd\u6570\u4e8c\u9636\u5bfc\u6570\u7684\u7b26\u53f7\u51b3\u5b9a\u8be5\u70b9\u662f\u6700\u5927\u503c\u8fd8\u662f\u6700\u5c0f\u503c\uff1a<\/span>\n<ul style=\"color:#64B5F6; font-weight: bold; margin-left:7%; list-style-type:circle\">\n<li style=\"margin-bottom:10px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u4e8c\u9636\u5bfc\u6570\u4e3a\u8d1f\uff0c\u5219\u51fd\u6570\u5728\u8be5\u70b9\u5177\u6709<strong>\u76f8\u5bf9\u6700\u5927\u503c<\/strong>\u3002<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-211c91be3bfe6e5a91f048684198c70a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(a)<0 \\quad \\bm{\\longrightarrow} \\quad x=a \\text{ es un m\\'aximo relativo}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"360\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:10px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u4e8c\u9636\u5bfc\u6570\u4e3a\u6b63\uff0c\u5219\u51fd\u6570\u5728\u8be5\u70b9\u5177\u6709<strong>\u76f8\u5bf9\u6700\u5c0f\u503c<\/strong>\u3002<\/span> <\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-089b7ae49fe440e3b4db19e0b17d8815_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(a)>0 \\quad \\bm{\\longrightarrow} \\quad x=a \\text{ es un m\\&#8217;inimo relativo}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;19&#8243; width=&#8221;356&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-como-calcular-los-maximos-y-minimos-de-una-funcion\"><\/span>\u793a\u4f8b 1\uff1a\u5982\u4f55\u8ba1\u7b97\u51fd\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u51fd\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u5c06\u9010\u6b65\u89e3\u51b3\u4e00\u4e2a\u793a\u4f8b\uff0c\u4ee5\u4fbf\u60a8\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u51fd\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u3002<\/p>\n<ul>\n<li>\u8ba1\u7b97\u4ee5\u4e0b\u51fd\u6570\u7684\u76f8\u5bf9\u6781\u503c\u5e76\u786e\u5b9a\u5b83\u4eec\u662f\u6700\u5927\u503c\u8fd8\u662f\u6700\u5c0f\u503c\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>\u51fd\u6570\u7684\u76f8\u5bf9\u6781\u503c\u5c06\u662f\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\u7684\u70b9<\/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-36700780d306ccf4975387990b1949fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9996\u5148\u8ba1\u7b97\u51fd\u6570\u7684\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-cad79f4ba702585c8bece2546419bd83_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>\u73b0\u5728\u6211\u4eec\u5c06\u51fd\u6570\u7684\u5bfc\u6570\u8bbe\u7f6e\u4e3a\u96f6\u5e76\u6c42\u89e3\u6240\u5f97\u7684\u4e8c\u6b21\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-36700780d306ccf4975387990b1949fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" 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-02ff903613a3329eb87c4943c4cb135b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x^2-3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"90\" 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-af1930d8be7faaf020a4103a17e484b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x^2=3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"59\" 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-e8367eba5249bf4e7b1e395d86bb91be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2=\\cfrac{3}{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"52\" 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-959000af33497314f9a59a9bed2a19c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2=1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"49\" 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-f0428d6e7e3932e00d3e6a7ab1a779d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= \\pm 1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u51fd\u6570\u7684\u76f8\u5bf9\u6781\u503c\u662f x=+1 \u548c x=-1\u3002<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u51fd\u6570\u7684\u76f8\u5bf9\u6781\u503c\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u901a\u8fc7\u4e8c\u9636\u5bfc\u6570\u7684\u7b26\u53f7\u77e5\u9053\u5b83\u4eec\u662f\u6700\u5927\u503c\u8fd8\u662f\u6700\u5c0f\u503c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u8ba1\u7b97\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-a2a906b229d6f4d4d03f59828f327fdb_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\u5728\u4e8c\u9636\u5bfc\u6570\u4e2d\u8bc4\u4f30\u6211\u4eec\u4e4b\u524d\u53d1\u73b0\u7684\u76f8\u5bf9\u6781\u503c\uff0c\u4ee5\u4e86\u89e3\u5b83\u4eec\u662f\u76f8\u5bf9\u6700\u5927\u503c\u8fd8\u662f\u6700\u5c0f\u503c\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-eb0c79376c0c8816492173e5f109809f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(1)=6\\cdot 1 = 6 \\ \\longrightarrow\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"167\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u76f8\u5bf9\u6700\u5c0f\u503c<\/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-8d51f54d437345293be122b03b5fff03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(-1)=6\\cdot (-1) = -6 \\ \\longrightarrow\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"222\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u6700\u5927\u76f8\u5bf9\u503c<\/p>\n<p>x=1 \u5904\u7684\u4e8c\u9636\u5bfc\u6570\u4e3a\u6b63\uff0c\u56e0\u6b64<strong>x=1 \u662f\u76f8\u5bf9\u6700\u5c0f\u503c<\/strong>\u3002\u53e6\u4e00\u65b9\u9762\uff0cx=-1 \u5904\u7684\u4e8c\u9636\u5bfc\u6570\u4e3a\u8d1f\uff0c\u56e0\u6b64<strong>x=-1 \u662f\u76f8\u5bf9\u6700\u5927\u503c<\/strong>\u3002<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5c06\u627e\u5230\u7684\u70b9\u4ee3\u5165\u539f\u59cb\u51fd\u6570\u4ee5\u627e\u5230\u76f8\u5bf9\u6781\u503c\u7684 Y \u5750\u6807\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-65771f8b9ce10ad863604fe6e6dca867_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1)=1^3-3\\cdot 1=-2 \\ \\longrightarrow \\ (1,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"275\" 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-04df1e45775b1318795100d7211f3b32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-1)=(-1)^3-3\\cdot(-1)= 2 \\ \\longrightarrow \\ (-1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"330\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u603b\u4e4b\uff0c\u51fd\u6570\u7684\u76f8\u5bf9\u6781\u503c\u662f\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u6700\u5c0f\u5230\u70b9<\/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-a80e956c137aedb103a56acc0cf510e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(1,-2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u6700\u5927\u63a5\u901a\u70b9<\/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-92defeed12f15814813d53b8a24be9ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-1,2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-estudiar-la-monotonia-y-los-maximos-y-minimos-de-una-funcion\"><\/span>\u793a\u4f8b 2\uff1a\u7814\u7a76\u51fd\u6570\u7684\u5355\u8c03\u6027\u4ee5\u53ca\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u770b\u770b\u53e6\u4e00\u79cd\u7ec3\u4e60\u662f\u5982\u4f55\u89e3\u51b3\u7684\u3002\u5728\u672c\u4f8b\u4e2d\uff0c\u6211\u4eec\u5c06\u89e3\u91ca\u5982\u4f55\u6839\u636e\u51fd\u6570\u7684\u5355\u8c03\u6027\u627e\u5230\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u3002<\/p>\n<ul>\n<li>\u7814\u7a76\u5355\u8c03\u6027\u5e76\u8ba1\u7b97\u4ee5\u4e0b\u51fd\u6570\u7684\u76f8\u5bf9\u6781\u503c\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-eb173dfd702785865be0051c9bcb7738_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x^2}{x-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"101\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u9996\u5148\u8981\u505a\u7684\u662f\u8ba1\u7b97\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3002\u4f5c\u4e3a\u6709\u7406\u51fd\u6570\uff0c\u6211\u4eec\u9700\u8981\u5c06\u5206\u6bcd\u8bbe\u7f6e\u4e3a 0 \u6765\u67e5\u770b\u54ea\u4e9b\u6570\u5b57\u4e0d\u5c5e\u4e8e\u51fd\u6570\u7684\u5b9a\u4e49\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-2a57ca6c48b6f646aeb64eb7f05e4840_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" 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-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-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-66d11e82f81cd2425ea2e6641e374baf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f= \\mathbb{R}-\\{1 \\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u8ba1\u7b97\u51fa\u51fd\u6570\u7684\u5b9a\u4e49\u57df\uff0c\u6211\u4eec\u5c31\u9700\u8981\u7814\u7a76\u54ea\u4e9b\u70b9\u62b5\u6d88\u4e00\u9636\u5bfc\u6570\u3002\u56e0\u6b64\u6211\u4eec\u63a8\u5bfc\u51fa\u51fd\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-19cfa0164864d95d9b2d51743bf7c0d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x^2}{x-1} \\ \\longrightarrow \\ f'(x)= \\cfrac{2x\\cdot (x-1) - x^2\\cdot 1}{\\left(x-1\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"364\" 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-8a280e333342dbe57e5d18839a1c9c0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{2x^2-2x - x^2}{\\left(x-1\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"172\" 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-8c77f1f797549bb4663fca07fcea2302_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{x^2-2x}{\\left(x-1\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"128\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5c06\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-36700780d306ccf4975387990b1949fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" 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-faf06fb85062e758f99800d1ffa0788b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^2-2x}{\\left(x-1\\right)^2}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"95\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p>\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-cc1f4cc53676f0eb98290b3478031fef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x-1\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -5px;\"><\/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-3d8bb0359e60db0b26d9bfce1b349e9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-2x=0\\cdot \\left(x-1\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"165\" 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-62138ee9fb8dc604ee836f1703379032_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-2x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u63d0\u53d6\u516c\u56e0\u5b50\u6765\u6c42\u89e3\u4e8c\u6b21\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-b243129a0d8853ec8716beb6d2d5c504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x(x-2)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\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\u4e3a 0\uff0c\u5e76\u5f97\u5230\u65b9\u7a0b\u7684\u4e24\u4e2a\u89e3\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-55127e675ce8f7742db17d565c2ae507_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle x\\cdot(x-2) =0   \\longrightarrow  \\begin{cases} \\bm{x=0} \\\\[2ex] x-2=0 \\ \\longrightarrow \\ \\bm{x= 2} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"329\" 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-36700780d306ccf4975387990b1949fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<p>\uff0c\u6211\u4eec\u8868\u793a\u7ebf\u4e0a\u627e\u5230\u7684\u6240\u6709\u5173\u952e\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\/ligne-numerique-0-1-2.webp\" alt=\"\" class=\"wp-image-2443\" width=\"399\" height=\"77\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u6211\u4eec\u8bc4\u4f30\u6bcf\u4e2a\u533a\u95f4\u5185\u5bfc\u6570\u7684\u7b26\u53f7\uff0c\u4ee5\u4e86\u89e3\u51fd\u6570\u662f\u589e\u52a0\u8fd8\u662f\u51cf\u5c11\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5728\u6bcf\u4e2a\u533a\u95f4\u4e2d\u53d6\u4e00\u4e2a\u70b9\uff08\u800c\u4e0d\u662f\u4e34\u754c\u70b9\uff09\u5e76\u67e5\u770b\u5bfc\u6570\u5728\u8be5\u70b9\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-8c77f1f797549bb4663fca07fcea2302_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{x^2-2x}{\\left(x-1\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"128\" 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-171fa182722405650545d6e7fe14d5b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(-1) = \\cfrac{(-1)^2-2(-1)}{\\left((-1)-1\\right)^2} =\\cfrac{+3}{+4} = +0,75 \\  \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"369\" 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-84e1013672adc10e9447af5478f592a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(0,5) = \\cfrac{0,5^2-2\\cdot0,5}{\\left(0,5-1\\right)^2} = \\cfrac{-0,75}{+0,25} = -3  \\  \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"363\" 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-110911aebecc81132e3d726e00be1fcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(1,5) = \\cfrac{1,5^2-2\\cdot1,5}{\\left(1,5-1\\right)^2} = \\cfrac{-0,75}{+0,25} = -3  \\  \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"363\" 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-b0a995a54cd7d661f6431cdc3d0d0eda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(3) = \\cfrac{3^2-2\\cdot3}{\\left(3-1\\right)^2} =\\cfrac{+3}{+4} = +0,75 \\  \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"313\" 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-0-1-2-positif-negatif-positif.webp\" alt=\"\" class=\"wp-image-2444\" width=\"400\" height=\"138\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u5982\u679c\u5bfc\u6570\u4e3a\u6b63\uff0c\u5219\u8868\u793a\u51fd\u6570\u5728\u589e\uff0c\u5982\u679c\u5bfc\u6570\u4e3a\u8d1f\uff0c\u5219\u8868\u793a\u51fd\u6570\u5728\u51cf\u3002\u56e0\u6b64\uff0c\u589e\u957f\u533a\u95f4\u548c\u4e0b\u964d\u533a\u95f4\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u751f\u957f\uff1a<\/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-11ebeca24ba262661dd73042a326110c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty, 0)\\cup (2,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u51cf\u5c11\uff1a<\/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-206ab3f38b17a58b25209bf269265919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(0,1)\\cup (1,2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b64\u5916\uff0c\u5f53 x=0 \u65f6\uff0c\u51fd\u6570\u4ece\u589e\u52a0\u53d8\u4e3a\u51cf\u5c11\uff0c\u56e0\u6b64<strong>x=0 \u662f\u51fd\u6570 \u7684\u76f8\u5bf9\u6700\u5927\u503c<\/strong><strong>\u3002<\/strong>\u5f53 x=2 \u65f6\uff0c\u51fd\u6570\u4ece\u9012\u51cf\u53d8\u4e3a\u9012\u589e\uff0c\u56e0\u6b64<strong>x=2 \u662f\u51fd\u6570\u7684\u76f8\u5bf9\u6700\u5c0f\u503c<\/strong>\u3002<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u66ff\u6362\u5728\u539f\u59cb\u51fd\u6570\u4e2d\u627e\u5230\u7684\u70b9\u6765\u627e\u5230\u7aef\u70b9\u7684 Y \u5750\u6807\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-d8bb02550f4c83abce02040f9e9ab495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(0)=\\cfrac{0^2}{0-1} = \\cfrac{0}{-1} = 0 \\ \\longrightarrow \\ (0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"268\" 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-74333ede5561c728c68899d68b31ee62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(2)=\\cfrac{2^2}{2-1} = \\cfrac{4}{1} = 4 \\ \\longrightarrow \\ (2,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"254\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c\u51fd\u6570\u7684\u76f8\u5bf9\u6781\u503c\u662f\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u6700\u5927\u63a5\u901a\u70b9<\/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-2c790019bd70403eba876c59c82c0f9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(0,0)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u6700\u5c0f\u5230\u70b9<\/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-a59b564601b4cd9f2bc149baa80c44a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(2,4)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-maximos-y-minimos-de-una-funcion\"><\/span>\u89e3\u51b3\u4e86\u51fd\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u7684\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\u76f8\u5bf9\u6781\u503c\u5e76\u786e\u5b9a\u5b83\u4eec\u662f\u6700\u5927\u503c\u8fd8\u662f\u6700\u5c0f\u503c\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-930d724a5ca23ed9152211f24dc2340b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-3x^2-9x\" 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\">\u51fd\u6570\u7684\u76f8\u5bf9\u6781\u503c\u662f\u51fd\u6570\u7684\u4e00\u9636\u5bfc\u6570\u4e3a\u96f6\u7684\u70b9\u3002\u56e0\u6b64\u6211\u4eec\u8ba1\u7b97\u51fd\u6570\u7684\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-f353678aff2ff5f19c53042f35ef8a19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-3x^2-9x \\ \\longrightarrow \\  f'(x)=3x^2-6x-9\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"376\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u89e3\u65b9\u7a0b<\/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-58dcd049349f740f082d583dfd9e364c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" 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-36700780d306ccf4975387990b1949fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" 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-77ac7ac1a36d5c8591235d8400eb68cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x^2-6x-9=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"131\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u6709\u4e00\u4e2a\u4e8c\u6b21\u65b9\u7a0b\uff0c\u6240\u4ee5\u6211\u4eec\u5e94\u7528\u4e00\u822c\u516c\u5f0f\u6765\u6c42\u89e3\u5b83\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-8e4a1d5ede3779d54c8b9b66571a3394_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} x &amp;=\\cfrac{-b \\pm \\sqrt{b^2-4ac}}{2a} =\\cfrac{-(-6) \\pm \\sqrt{(-6)^2-4\\cdot 3 \\cdot (-9)}}{2\\cdot 3}=\\\\[1.5ex]&amp;=\\cfrac{6 \\pm \\sqrt{144}}{6}=\\cfrac{6 \\pm 12}{6} =\\begin{cases} \\cfrac{6 + 12}{6}=\\cfrac{18}{6}= 3 \\\\[4ex] \\cfrac{6 - 12}{6}=\\cfrac{-6}{6}=-1 \\end{cases} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"168\" width=\"451\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u51fd\u6570\u7684\u76f8\u5bf9\u6781\u503c\u662f\u70b9 x=3 \u548c x=-1\u3002<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u51fd\u6570\u7684\u76f8\u5bf9\u6781\u503c\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u901a\u8fc7\u4e8c\u9636\u5bfc\u6570\u7684\u7b26\u53f7\u77e5\u9053\u5b83\u4eec\u662f\u6700\u5927\u503c\u8fd8\u662f\u6700\u5c0f\u503c\u3002\u56e0\u6b64\u6211\u4eec\u518d\u6b21\u5bf9\u51fd\u6570\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-b2ddaaae5740b93b84eb1db4c4e12f69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=3x^2-6x-9 \\ \\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\u7528\u4e8c\u9636\u5bfc\u6570\u8ba1\u7b97\u4e4b\u524d\u8ba1\u7b97\u7684\u70b9\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-b97f883eb74286ab41179d4353161816_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(3)=6(3)-6=18-6 = +12 \\ \\longrightarrow \\ \\text{M\\'inimo}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"365\" 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-b6efbeb4ad4b54c03aa440dcafb7dc4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(-1)=6(-1)-6=-6-6 = -12 \\ \\longrightarrow \\ \\text{M\\'aximo}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"400\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> x=3 \u5904\u7684\u4e8c\u9636\u5bfc\u6570\u4e3a\u6b63\uff0c\u56e0\u6b64<strong>x=3 \u662f\u6700\u5c0f\u503c<\/strong>\u3002 x=-1 \u5904\u7684\u4e8c\u9636\u5bfc\u6570\u4e3a\u8d1f\uff0c\u56e0\u6b64<strong>x=-1 \u662f\u6700\u5927\u503c<\/strong>\u3002<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u66ff\u6362\u5728\u539f\u59cb\u51fd\u6570\u4e2d\u627e\u5230\u7684\u70b9\u6765\u627e\u5230\u7aef\u70b9\u7684 Y \u5750\u6807\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-0b885b81db85c9d12caeed0e046f14ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(3)=3^3-3\\cdot 3^2-9\\cdot3=-27 \\ \\longrightarrow \\ (3,-27)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"353\" 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-668346639ebe571949cd8e8939c8a4a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-1)=(-1)^3-3(-1)^2-9(-1)=5 \\ \\longrightarrow \\ (-1,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"392\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7b80\u800c\u8a00\u4e4b\uff0c\u51fd\u6570\u7684\u76f8\u5bf9\u6781\u503c\u662f\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u76f8\u5bf9\u4e8e\u70b9\u7684\u6700\u5c0f\u503c<\/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-1b572e4ffbdfe59c16e4e1a30b9ac82a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(3,-27)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u76f8\u5bf9\u4e8e\u70b9\u7684\u6700\u5927\u503c<\/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-c7aca1cad23e01f6998ce87ff4f73734_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-1,5)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" 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>\u8ba1\u7b97\u4ee5\u4e0b\u6307\u6570\u51fd\u6570\u7684\u76f8\u5bf9\u6781\u503c\u5e76\u786e\u5b9a\u5b83\u4eec\u662f\u6700\u5927\u503c\u8fd8\u662f\u6700\u5c0f\u503c\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-6e82a7f154d9620b6fdcd2d134cbf20a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=e^x(x-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" 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\">\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u533a\u5206\u51fd\u6570\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5e94\u7528\u4e58\u79ef\u5bfc\u6570\u7684\u516c\u5f0f\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-5508d7a8f5ef73fd09e2c8a013513229_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=e^x\\cdot (x-1)+ e^x\\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"206\" 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-6d1f83cd5953e56070c9f8dea5a03ea5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=xe^x -e^x +e^x = xe^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"216\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u89e3\u65b9\u7a0b<\/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-58dcd049349f740f082d583dfd9e364c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" 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-36700780d306ccf4975387990b1949fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" 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-9da9b4b19b1c7985bf785b693009de95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"xe^x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"60\" 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-f5c0d99b3aa4115c0415e0e57f5df2a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle x\\cdot e^x =0 \\longrightarrow \\begin{cases} \\bm{x=0} \\\\[2ex] e^x=0 \\ \\color{red}\\bm{\\times} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"220\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u4e2a\u6570\u4e58\u4ee5\u53e6\u4e00\u4e2a\u6570\u6c38\u8fdc\u4e0d\u4f1a\u5f97\u5230 0\u3002\u56e0\u6b64\uff0c<\/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-0108040ee23df4da2db681c9ffb2decc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e^x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u65e0\u89e3\uff0c\u552f\u4e00\u76f8\u5bf9\u6781\u7aef\u7684\u662f<\/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>\u3002<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u8ba1\u7b97\u51fd\u6570\u7684\u4e8c\u9636\u5bfc\u6570\u6765\u77e5\u9053\u76f8\u5bf9\u6781\u503c\u662f\u6700\u5927\u503c\u8fd8\u662f\u6700\u5c0f\u503c\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-2e3186824ec757b18335f7c6b93e6068_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)= xe^x \\ \\longrightarrow \\ f''(x)= 1\\cdot e^x + x \\cdot e^x = e^x+xe^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"394\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u7528\u4e8c\u9636\u5bfc\u6570\u8bc4\u4f30\u6211\u4eec\u4e4b\u524d\u53d1\u73b0\u7684\u6781\u503c\uff0c\u770b\u770b\u5b83\u662f\u6700\u5927\u503c\u8fd8\u662f\u6700\u5c0f\u503c\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-a333c6f36d372595070b5cf10ef06659_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(0)= e^{0}+0\\cdot e^{0} = 1+0\\cdot 1 = 1 \\ \\longrightarrow \\ \\text{M\\'inimo}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"368\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e x=0 \u5904\u7684\u4e8c\u9636\u5bfc\u6570\u4e3a\u6b63\uff0c<strong>\u56e0\u6b64 x=0 \u662f\u76f8\u5bf9\u6700\u5c0f\u503c\u6216\u5c40\u90e8\u6700\u5c0f\u503c<\/strong>\u3002<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u7528\u539f\u51fd\u6570\u4e2d\u627e\u5230\u7684\u70b9\u6765\u6c42\u51fa\u53e6\u4e00\u7aef\u5750\u6807\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-b262d8c03601983b5497fc165bab677a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(0)=e^{0}(0-1) =1\\cdot (-1)=-1 \\ \\longrightarrow \\ (0,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"357\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u7684\u552f\u4e00\u76f8\u5bf9\u6781\u503c\u662f\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u6700\u5c0f\u5230\u70b9<\/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-737e35e6d1698a9e89986af90d34722e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(0,-1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" 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>\u7814\u7a76\u5355\u8c03\u6027\u5e76\u627e\u5230\u4ee5\u4e0b\u6709\u7406\u51fd\u6570\u7684\u76f8\u5bf9\u6781\u503c\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-03ea07dcfe35eeade4235b3325681c2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{x -1 }{x^2+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"109\" style=\"vertical-align: -14px;\"><\/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\uff0c\u6211\u4eec\u786e\u5b9a\u51fd\u6570\u7684\u57df\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u5206\u6570\u7684\u5206\u6bcd\u8bbe\u7f6e\u4e3a\u96f6\u5e76\u6c42\u89e3\u6240\u5f97\u7684\u4e8c\u6b21\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-13670326c7cf3ae27c79e8e2ea4f438b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+1 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"81\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8868\u8fbe\u65b9\u5f0f<\/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-b35b5141a240a76c5fc0e3c75ab5689d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+1\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"47\" style=\"vertical-align: -2px;\"><\/p>\n<p>\u5b83\u6c38\u8fdc\u4e0d\u4f1a\u662f 0\uff0c\u56e0\u4e3a x <sup>2<\/sup>\u7684\u7ed3\u679c\u59cb\u7ec8\u662f\u6b63\u6570\u6216 0\u3002\u56e0\u6b64\uff0c\u52a0 1 \u6c38\u8fdc\u4e0d\u4f1a\u5f97\u5230 0\u3002\u56e0\u6b64\uff0c\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u4ec5\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\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u7814\u7a76\u54ea\u4e9b\u70b9\u7b26\u5408<\/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-3d9516fab46f301bc09e336a12418ad4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=0.\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u6211\u4eec\u4f7f\u7528\u5546\u89c4\u5219\u5bf9\u51fd\u6570\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-2a21eceaf556455939314d569b69f365_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x -1 }{x^2+1} \\ \\longrightarrow \\ f'(x)= \\cfrac{1 \\cdot (x^2+1) - (x-1) \\cdot 2x }{\\left(x^2+1}\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"415\" 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-6104d51f83e54587e198db396734fec1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)= \\cfrac{x^2+1-(2x^2-2x)}{\\left(x^2+1\\right)^2} = \\cfrac{x^2+1-2x^2+2x}{\\left(x^2+1\\right)^2}= \\cfrac{-x^2+2x+1}{\\left(x^2+1\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"515\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\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-4890b9dfeb634c4d7a349351be73b5d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" 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-501383d3407e95ff1980351452e414f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{-x^2+2x+1}{\\left(x^2+1\\right)^2}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"143\" 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-348057b71ce15780c2f47bd8053e4cd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-x^2+2x+1=0\\cdot \\left(x^2+1\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"219\" 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-579207dec3599e2925ad24d2e951cb47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-x^2+2x+1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"134\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u6709\u4e00\u4e2a\u4e8c\u6b21\u65b9\u7a0b\uff0c\u6240\u4ee5\u6211\u4eec\u7528\u4e00\u822c\u516c\u5f0f\u6765\u6c42\u89e3\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-836d878f15098c1fe997fbb0392b8733_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}x &amp;=\\cfrac{-b \\pm \\sqrt{b^2-4ac}}{2a} =\\cfrac{-2 \\pm \\sqrt{2^2-4\\cdot (-1) \\cdot 1}}{2\\cdot (-1)} = \\\\[1.5ex]&amp;=\\cfrac{-2 \\pm \\sqrt{8}}{-2} =\\begin{cases} \\cfrac{-2 + \\sqrt{8}}{-2}= -0,41 \\\\[4ex] \\cfrac{-2 - \\sqrt{8}}{-2}= 2,41\\end{cases} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"174\" width=\"396\" 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\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-36700780d306ccf4975387990b1949fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" 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\/number-line-041-241.webp\" alt=\"\" class=\"wp-image-2451\" width=\"319\" height=\"83\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u8bc4\u4f30\u6bcf\u4e2a\u533a\u95f4\u5185\u5bfc\u6570\u7684\u7b26\u53f7\uff0c\u4ee5\u786e\u5b9a\u51fd\u6570\u662f\u9012\u589e\u8fd8\u662f\u9012\u51cf\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5728\u6bcf\u4e2a\u533a\u95f4\u4e2d\u53d6\u4e00\u4e2a\u70b9\uff08\u800c\u4e0d\u662f\u5947\u70b9\uff09\u5e76\u67e5\u770b\u6b64\u65f6\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-6c9e9690a2834e9ba455ebe711bfba4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(-1)= \\cfrac{-(-1)^2+2(-1)+1}{\\left((-1)^2+1\\right)^2}}= \\cfrac{-2}{+4} =-0,5 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"412\" 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-6c280aa192cd61431df6a1ade0389ed2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(0)= \\cfrac{-0^2+2(0)+1}{\\left(0^2+1\\right)^2}}= \\cfrac{+1}{+1} =+1 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"340\" 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-b40b424c7a763aa9849f33d850a10a1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(3)= \\cfrac{-3^2+2\\cdot 3+1}{\\left(3^2+1\\right)^2}}= \\cfrac{-2}{+100} =-0,02 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"375\" 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-041-241-negatif-positif-negatif.webp\" alt=\"\" class=\"wp-image-2453\" width=\"319\" height=\"150\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u5982\u679c\u5bfc\u6570\u4e3a\u6b63\uff0c\u5219\u8868\u793a\u51fd\u6570\u5728\u8be5\u533a\u95f4\u5185\u9012\u589e\uff0c\u4f46\u5982\u679c\u5bfc\u6570\u4e3a\u8d1f\uff0c\u5219\u8868\u793a\u51fd\u6570\u5728\u9012\u51cf\u3002\u56e0\u6b64\uff0c\u589e\u957f\u533a\u95f4\u548c\u4e0b\u964d\u533a\u95f4\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u751f\u957f\uff1a<\/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-262e8d5f95ee4afe2dacc0037d8f334c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-0,41 \\ , \\ 2,41)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u51cf\u5c11\uff1a<\/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-33c3a6bfd3dbfbdd2eff5fc4b70aea5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty \\ , \\ -0,41)\\cup (2,41 \\ , \\ +\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"231\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728 x=-0.41 \u5904\uff0c\u51fd\u6570\u4ece\u9012\u51cf\u53d8\u4e3a\u9012\u589e\uff0c\u56e0\u6b64<strong>x=-0.41 \u662f\u51fd\u6570\u7684\u5c40\u90e8\u6700\u5c0f\u503c<\/strong>\u3002\u5e76\u4e14\u51fd\u6570\u5728 x=2.41 \u5904\u4ece\u589e\u52a0\u53d8\u4e3a\u51cf\u5c11\uff0c\u56e0\u6b64<strong>x=2.41 \u662f\u8be5\u51fd\u6570\u7684\u5c40\u90e8\u6700\u5927\u503c<\/strong>\u3002<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u5c06\u627e\u5230\u7684\u6781\u503c\u4ee3\u5165\u539f\u59cb\u51fd\u6570\u4ee5\u6c42\u51fa\u70b9\u7684 Y \u5750\u6807\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-605a64bba8103c7ee0015a92b60273b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-0,41)=\\cfrac{-0,41 -1 }{(-0,41)^2+1} = \\cfrac{-1,41}{1,17}= -1,21 \\ \\longrightarrow \\ (-0,41 \\ , \\ -1,21)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"532\" style=\"vertical-align: -17px;\"><\/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-02ff38a48dc66cf3a658619cf41803c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(2,41)=\\cfrac{2,41 -1 }{2,41^2+1} = \\cfrac{1,41}{6,81}= 0,21 \\ \\longrightarrow \\ (2,41 \\ , \\ 0,21)\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"427\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u7684\u76f8\u5bf9\u6781\u503c\u662f\uff1a<\/p>\n<p class=\"has-text-align-center\"><strong>\u6700\u5c0f\u5230\u70b9<\/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-906261d9a75f4bc2766c65fc0ac5a363_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-0,41 \\ , \\ -1,21)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><strong>\u6700\u5927\u63a5\u901a\u70b9<\/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-bf7380f280bd665935068801c9c0d83d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{ (2,41 \\ , \\ 0,21)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" 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\u4e604<\/h3>\n<p>\u6211\u4eec\u77e5\u9053\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-bc79cbc1c7886fe5d95d2db47d1635f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2+ax+b\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"147\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u901a\u8fc7\u70b9<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8f97f2fdc4d62902377daa83ebbd005b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u5e76\u4e14\u6709\u4e00\u4e2a\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-3d8c9d56ee018947d8f054cd237e8c06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1 .\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u786e\u5b9a\u672a\u77e5\u6570\u7684\u503c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c\u4ef7\u503c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-73a3ea89ad967f2efadeb096bd87bdb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b .\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/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\">\u4ee4\u51fd\u6570\u6709\u76f8\u5bf9\u6781\u503c<\/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-ee848c4f59793dbd8bd705b4e2411c8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u8fd9\u610f\u5473\u7740\u5b83\u5df2\u7ecf\u5b8c\u6210\u4e86<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f57b701a1080acd4db5681249566b5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(-1)=0.\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u8ba1\u7b97\u51fd\u6570\u7684\u5bfc\u6570<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ee848c4f59793dbd8bd705b4e2411c8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6211\u4eec\u5c06\u5176\u8bbe\u7f6e\u4e3a 0\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-41316f1389c40d8634eb0ad596956ca2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = x^2+ax+b \\ \\longrightarrow \\ f'(x)=2x+a\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"309\" 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-1786074f9a3b69a0c2a13a0db7a67895_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} f'(-1)=2(-1)+a\\\\[2ex] f'(-1)=0\\end{array} \\right\\} \\longrightarrow 2(-1)+a=0\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u6c42\u89e3\u5f97\u5230\u7684\u65b9\u7a0b\u6765\u627e\u5230\u53c2\u6570a\u7684\u503c\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-f5e35d6b05179bb3e4db43f738b6da29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2(-1)+a=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" 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-729fe80252784c84b2a49624e59b2ac7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2+a=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"85\" 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-85d78ced37b5f76e83a3c9c24a8b3eca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{a=2}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u5c06\u662f\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-bbea1a44d5027753ebc196d004e5671d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2+ax+b \\ \\xrightarrow{a \\ = \\ 2} \\ f(x)=x^2+2x+b\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"362\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u4ed6\u4eec\u544a\u8bc9\u6211\u4eec\u51fd\u6570\u901a\u8fc7\u70b9<\/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-702446e4df1457eff7e83e00a8709824_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1,-2) .\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-304a45b518ffaec62b95f169ad647688_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1)=-2 .\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5e94\u7528\u8fd9\u4e2a\u6761\u4ef6\u6765\u6c42\u53d8\u91cf b \u7684\u503c\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-6c09bb57a4a4fd3eb5d72f5d35d3c539_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} f(1)=1^2+2\\cdot1+b \\\\[2ex] f(1)=-2 \\end{array} \\right\\} \\longrightarrow 1^2+2\\cdot 1+b = -2\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"361\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u6c42\u89e3\u5f97\u5230\u7684\u65b9\u7a0b\u6765\u627e\u5230\u53c2\u6570 b \u7684\u503c\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-4e05b252664d0ea2da72627e779469d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1^2+2\\cdot1+b=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"143\" 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-626f95581121d205b149c2323e711759_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1+2+b=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"113\" 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-625149278867f4929d813258055868e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b=-2-1-2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"114\" 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-2e925fb7c5eaa30caa970c92688ede93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{b=-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"53\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\u8be5\u51fd\u6570\u4e3a\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-2becf12662d9dc5f68cb13dd248f3e51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2+2x+b \\ \\xrightarrow{b \\ = \\ -5} \\ f(x)=x^2+2x-5\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"371\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u51fd\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u4e24\u4e2a\u793a\u4f8b\u6765\u5411\u60a8\u89e3\u91ca\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u9010\u6b65\u7ec3\u4e60\u51fd &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%87%bd%e6%95%b0%e7%9b%b8%e5%af%b9%e6%9e%81%e5%80%bc%e7%9a%84%e6%9e%81%e5%a4%a7%e6%9e%81%e5%b0%8f%e5%80%bc\/\"> <span class=\"screen-reader-text\">\u51fd\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\uff08\u76f8\u5bf9\u6781\u503c\uff09<\/span> \u67e5\u770b\u5168\u6587 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[17],"tags":[],"class_list":["post-43","post","type-post","status-publish","format-standard","hentry","category-17"],"yoast_head":"<!-- This site is optimized 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