{"id":357,"date":"2023-07-04T11:55:40","date_gmt":"2023-07-04T11:55:40","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%be%b7%e5%a8%81%e5%b0%94%e6%96%af%e7%89%b9%e6%8b%89%e6%96%af%e5%ae%9a%e7%90%86\/"},"modified":"2023-07-04T11:55:40","modified_gmt":"2023-07-04T11:55:40","slug":"%e5%be%b7%e5%a8%81%e5%b0%94%e6%96%af%e7%89%b9%e6%8b%89%e6%96%af%e5%ae%9a%e7%90%86","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%be%b7%e5%a8%81%e5%b0%94%e6%96%af%e7%89%b9%e6%8b%89%e6%96%af%e5%ae%9a%e7%90%86\/","title":{"rendered":"\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406"},"content":{"rendered":"

\u5728\u672c\u6587\u4e2d\uff0c\u60a8\u5c06\u627e\u5230\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u7684\u5b9a\u4e49\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u7684\u51e0\u4e2a\u7ec3\u4e60\u6765\u8fdb\u884c\u7ec3\u4e60\uff0c\u4ee5\u5b8c\u7f8e\u5730\u7406\u89e3\u5b83\u3002 <\/p>\n

<\/span>\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u7684\u9648\u8ff0<\/span><\/h2>\n

\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u6307\u51fa\uff0c\u5982\u679c\u51fd\u6570\u5728\u95ed\u533a\u95f4\u4e0a\u8fde\u7eed\uff0c\u5219\u8be5\u51fd\u6570\u5728\u8be5\u533a\u95f4\u4e0a\u5177\u6709\u7edd\u5bf9\u6700\u5927\u503c\u548c\u7edd\u5bf9\u6700\u5c0f\u503c\u3002<\/strong><\/p>\n

\u27a4<\/span>\u8bf7\u53c2\u9605\uff1a<\/strong> \u4ec0\u4e48\u662f\u8fde\u7eed\u51fd\u6570\uff1f<\/a><\/span><\/p>\n

\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u53ea\u6307\u51fa\u5b58\u5728\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\uff0c\u4f46\u8ba1\u7b97\u8fd9\u4e9b\u70b9\u7684\u503c\u5e76\u6ca1\u6709\u4ec0\u4e48\u7528\u5904\u3002 <\/p>\n

\n
\"\u97e6\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\"<\/figure>\n<\/div>\n

\u4f8b\u5982\uff0c\u4e0a\u9762\u7ed8\u5236\u7684\u51fd\u6570\u5728\u533a\u95f4 [a,b] \u4e0a\u662f\u8fde\u7eed\u7684\uff0c\u5e76\u4e14\u5728\u6b64\u533a\u95f4\u4e0a\u5177\u6709\u6700\u5c0f\u503c\u548c\u6700\u5927\u503c\u3002\u867d\u7136\u6211\u4eec\u65e0\u6cd5\u77e5\u9053\u8fd9\u4e24\u70b9\u7684\u51c6\u786e\u5750\u6807\uff0c\u4f46\u6211\u4eec\u77e5\u9053\u51fd\u6570\u5728\u533a\u95f4\u5185\u6709\u8fd9\u4e24\u4e2a\u7aef\u70b9\u3002<\/p>\n

\u27a4<\/span>\u8bf7\u53c2\u9605\uff1a<\/strong> \u5982\u4f55\u8ba1\u7b97\u51fd\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c<\/a><\/span><\/p>\n

\u7531\u4e8e\u8be5\u51fd\u6570\u5728\u6574\u4e2a\u533a\u95f4\u5185\u662f\u8fde\u7eed\u7684\uff0c\u8fd9\u610f\u5473\u7740\u5b83\u8fd8\u5c06\u5728\u540c\u4e00\u533a\u95f4\u5185\u53d6\u7edd\u5bf9\u6700\u5c0f\u503c\u548c\u7edd\u5bf9\u6700\u5927\u503c\u4e4b\u95f4\u7684\u6240\u6709\u53ef\u80fd\u503c\u3002<\/p>\n

\u6b64\u5916\uff0c\u6839\u636e\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\uff0c\u6211\u4eec\u53ef\u4ee5\u63a8\u65ad\u51fa\u95ed\u533a\u95f4\u4e0a\u7684\u4efb\u4f55\u8fde\u7eed\u51fd\u6570\u90fd\u5728\u7684\u4e0a\u65b9\u548c\u4e0b\u65b9\u6709\u754c<\/strong>\uff0c\u5e76\u4e14\u51fd\u6570\u7684\u4e0a\u9650\u548c\u4e0b\u9650\u5206\u522b\u662f\u7edd\u5bf9\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u3002<\/p>\n

\u5728\u6570\u5b66\u4e0a\uff0c\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u53ef\u4ee5\u8868\u8fbe\u5982\u4e0b\uff1a<\/p>\n<\/p>\n

\"f(x_1)\\leq<\/p>\n<\/p>\n

\u91d1\u5b50<\/p>\n<\/p>\n

\"x_1\"<\/p>\n

\u548c<\/p>\n

\"x_2\"<\/p>\n

\u662f\u95ed\u533a\u95f4\u4e2d\u5305\u542b\u7684\u4e24\u4e2a\u70b9\uff08\u5206\u522b\u662f\u7edd\u5bf9\u6700\u5c0f\u503c\u548c\u7edd\u5bf9\u6700\u5927\u503c\uff09<\/p>\n

\"[a,b]\"<\/p>\n

\u5176\u4e2d\u5b9a\u4e49\u4e86\u8be5\u51fd\u6570\u3002<\/p>\n

\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u7684\u8bc1\u660e\u76f8\u5f53\u590d\u6742\uff0c\u5bf9\u6982\u5ff5\u7684\u8d21\u732e\u4e0d\u5927\uff0c\u6240\u4ee5\u672c\u6587\u4e0d\u505a\u89e3\u91ca\u3002\u91cd\u8981\u7684\u662f\u4f60\u8981\u4e86\u89e3\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u7684\u7528\u9014\u3002 <\/p>\n

<\/span>\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u89e3\u51b3\u7684\u95ee\u9898<\/span><\/h2>\n

\u7ec3\u4e601<\/h3>\n

\u786e\u5b9a\u4ee5\u4e0b\u51fd\u6570\u662f\u5426\u6709\u754c\u4e8e\u5efa\u8bae\u7684\u533a\u95f4\uff1a<\/p>\n<\/p>\n

\"f(x)=\\log_3(x-4)<\/p>\n<\/p>\n

\u27a4<\/span>\u8bf7\u53c2\u9605\uff1a<\/strong>\u5bf9\u6570\u51fd\u6570\u7684\u57df<\/a><\/span><\/p>\n

\n
\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n

\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5e94\u7528 Weierstrass \u5b9a\u7406\u6765\u786e\u5b9a\u51fd\u6570\u662f\u5426\u5728\u533a\u95f4 [5,10] \u4e0a\u6709\u754c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u77e5\u9053\u51fd\u6570\u5728\u6b64\u533a\u95f4\u5185\u662f\u5426\u8fde\u7eed\uff0c\u4e3a\u6b64\uff0c\u6211\u4eec\u8ba1\u7b97\u5bf9\u6570\u51fd\u6570\u7684\u57df\uff1a <\/p>\n<\/p>\n

\"x-40″ title=”Rendered by QuickLaTeX.com” height=”14″ width=”73″ style=”vertical-align: -2px;”><\/p>\n<\/p>\n

\"x4″ title=”Rendered by QuickLaTeX.com” height=”14″ width=”43″ style=”vertical-align: -2px;”><\/p>\n<\/p>\n

\"\\text{Dom<\/p>\n<\/p>\n

\u8be5\u51fd\u6570\u5bf9\u4e8e\u6240\u6709\u5927\u4e8ex=4\u7684\u503c\u90fd\u662f\u8fde\u7eed\u7684\uff0c\u56e0\u6b64\u5b83\u5728\u533a\u95f4[5,10]\u4e0a\u8fde\u7eed\u3002<\/p>\n

\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u6ee1\u8db3\u533a\u95f4 [5,10] \u4e0a\u7684\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\uff0c\u8fd9\u610f\u5473\u7740\u5b83\u5728\u6b64\u533a\u95f4\u7684\u4e0a\u4e0b\u6709\u754c\u3002<\/p>\n

<\/div>\n

\u7ec3\u4e602<\/h3>\n

\u786e\u5b9a\u4ee5\u4e0b\u51fd\u6570\u5728\u5efa\u8bae\u7684\u533a\u95f4\u5185\u662f\u5426\u5177\u6709\u6700\u5927\u503c\u548c\/\u6216\u6700\u5c0f\u503c\uff1a<\/p>\n<\/p>\n

\"f(x)=\\cfrac{3x^2-4}{2x-4}<\/p>\n<\/p>\n

\u27a4<\/span>\u8bf7\u53c2\u9605\uff1a<\/strong>\u6709\u7406\u51fd\u6570\u7684\u57df<\/a><\/span><\/p>\n

\n
\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n

\u9996\u5148\u6211\u4eec\u5206\u6790\u6709\u7406\u51fd\u6570\u7684\u8fde\u7eed\u6027\uff1a <\/p>\n<\/p>\n

\"2x-4=0\"<\/p>\n<\/p>\n

\"2x=4\"<\/p>\n<\/p>\n

\"x=\\cfrac{4}{2}=2\"<\/p>\n<\/p>\n

\"\\text{Dom<\/p>\n<\/p>\n

\u7136\u800c\uff0c\u8be5\u51fd\u6570\u5728 x=2 \u5904\u5448\u73b0\u4e0d\u8fde\u7eed\u6027\uff0c\u8fd9\u610f\u5473\u7740\u5b83\u5728\u533a\u95f4 [-3,3] \u4e0a\u4e0d\u8fde\u7eed\u3002<\/p>\n

\u7b80\u800c\u8a00\u4e4b\uff0c\u8be5\u51fd\u6570\u4e0d\u6ee1\u8db3\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\uff0c\u56e0\u6b64\u6211\u4eec\u4e0d\u80fd\u8bf4\u5b83\u5728\u8be5\u533a\u95f4\u5185\u662f\u5426\u5177\u6709\u6700\u5c0f\u503c\u6216\u6700\u5927\u503c\u3002<\/p>\n

<\/div>\n

\u7ec3\u4e603<\/h3>\n

\u786e\u5b9a\u4ee5\u4e0b\u51fd\u6570\u5728\u5efa\u8bae\u7684\u533a\u95f4\u5185\u662f\u5426\u5177\u6709\u6700\u5927\u503c\u548c\/\u6216\u6700\u5c0f\u503c\u5e76\u8ba1\u7b97\u8fd9\u4e9b\u70b9\uff1a<\/p>\n<\/p>\n

\"f(x)=x^2+3<\/p>\n<\/p>\n

\u27a4<\/span>\u53c2\u89c1\uff1a<\/strong>\u4e8c\u6b21\u51fd\u6570\u7684\u7279\u5f81<\/a><\/span><\/p>\n

\n
\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n

\u4efb\u4f55\u4e8c\u6b21\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u90fd\u662f\u5b9e\u6570\uff1a<\/p>\n<\/p>\n

\"\\text{Dom<\/p>\n<\/p>\n

\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u5728\u533a\u95f4 [0,4] \u4e0a\u8fde\u7eed\u5e76\u4e14\u6ee1\u8db3 Weierstrass \u5b9a\u7406\u3002\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u5728\u6b64\u533a\u95f4\u4e0a\u5177\u6709\u7edd\u5bf9\u6700\u5c0f\u503c\u548c\u7edd\u5bf9\u6700\u5927\u503c\u3002<\/p>\n

\u6b64\u5916\uff0c\u8be5\u629b\u7269\u7ebf\u7684\u9876\u70b9\u6070\u597d\u4f4d\u4e8e x=0 \u5904\uff0c\u56e0\u6b64\u8be5\u51fd\u6570\u5728\u533a\u95f4 [0,4] \u4e0a\u4e25\u683c\u9012\u589e\uff0c\u56e0\u6b64\u6700\u5c0f\u503c\u4f4d\u4e8e x=0 \u5904\uff0c\u6700\u5927\u503c\u4f4d\u4e8e x= 4 \u5904\u3002 <\/p>\n<\/p>\n

\"\\text{M\\'inimo<\/p>\n<\/p>\n

\"\\text{M\\'aximo<\/p>\n<\/p>\n

<\/div>\n

<\/span>\u5361\u5c14\u00b7\u7ef4\u5c14\u65af\u7279\u62c9\u65af<\/span><\/h2>\n

\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u7684\u542b\u4e49\uff0c\u6211\u4eec\u5c06\u7b80\u8981\u89e3\u91ca\u8be5\u5b9a\u7406\u7684\u53d1\u660e\u8005\u662f\u8c01\u3002<\/p>\n

\u5361\u5c14\u00b7\u897f\u5965\u591a\u00b7\u5a01\u5ec9\u00b7\u7ef4\u5c14\u65af\u7279\u62c9\u65af<\/strong>\u662f19\u4e16\u7eaa\u5fb7\u56fd\u4e00\u4f4d\u975e\u5e38\u91cd\u8981\u7684\u6570\u5b66\u5bb6\uff0c\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u4ed6\u4e8e1815\u5e7410\u670831\u65e5\u51fa\u751f\u4e8e\u5965\u65af\u5766\u8d39\u5c14\u5fb7\uff0c\u4e8e1897\u5e742\u670819\u65e5\u901d\u4e16\u4e8e\u67cf\u6797\u3002<\/p>\n

\u9664\u4e86\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u5916\uff0c\u4ed6\u8fd8\u56e0\u5176\u5bf9\u6570\u5b66\u7684\u5176\u4ed6\u8d21\u732e\u800c\u95fb\u540d\u3002\u5176\u4e2d\uff0c\u4ed6\u7ed9\u51fa\u4e86\u51fd\u6570\u7684\u4e09\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u6982\u5ff5\u8fde\u7eed\u6027\u3001\u6781\u9650\u548c\u5bfc\u6570\u7684\u5b9a\u4e49\u3002<\/p>\n

\u540c\u6837\uff0c\u4ed6\u6210\u529f\u5730\u8bc1\u660e\u4e86\u5f53\u65f6\u5c1a\u672a\u5728\u6570\u5b66\u4e0a\u9a8c\u8bc1\u7684\u67d0\u4e9b\u5b9a\u7406\uff0c\u4f8b\u5982\u535a\u5c14\u624e\u8bfa-\u97e6\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u3001\u4e2d\u503c\u5b9a\u7406\u6216\u6d77\u6d85-\u535a\u96f7\u5c14\u5b9a\u7406\u3002<\/p>\n

\u4ee4\u4eba\u597d\u5947\u7684\u662f\uff0c\u6709\u4e00\u4e2a\u6708\u7403\u9668\u77f3\u5751\u548c\u4e00\u9897\u5c0f\u884c\u661f\u4ee5\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u7684\u540d\u5b57\u547d\u540d\uff0c\u4ee5\u7eaa\u5ff5\u4ed6\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

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