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\u300a\u9ad8\u7b49\u6570\u5b66\u300b\u8003\u8bd5\u5927\u7eb2<\/p>\n
\u8003\u8bd5\u8981\u6c42
\n\u8003\u751f\u5e94\u6309\u672c\u5927\u7eb2\u7684\u8981\u6c42\uff0c\u638c\u63e1\u201c\u9ad8\u7b49\u6570\u5b66\u201d\u4e2d\u51fd\u6570\u3001\u6781\u9650\u548c\u8fde\u7eed\u3001\u4e00\u5143\u51fd\u6570\u5fae\u5206\u5b66\u3001\u4e00\u5143\u51fd\u6570\u79ef\u5206\u5b66\u3001\u65e0\u7a77\u7ea7\u6570\u3001\u5e38\u5fae\u5206\u65b9\u7a0b\u3001\u5411\u91cf\u4ee3\u6570\u4e0e\u7a7a\u95f4\u89e3\u6790\u51e0\u4f55\u7684\u57fa\u672c\u6982\u5ff5\u3001\u57fa\u672c\u7406\u8bba\u548c\u57fa\u672c\u65b9\u6cd5\u3002\u8003\u751f\u5e94\u6ce8\u610f\u5404\u90e8\u5206\u77e5\u8bc6\u7684\u7ed3\u6784\u53ca\u77e5\u8bc6\u7684\u8054\u7cfb\uff1b\u5177\u6709\u4e00\u5b9a\u7684\u62bd\u8c61\u601d\u7ef4\u80fd\u529b\u3001\u903b\u8f91\u63a8\u7406\u80fd\u529b\u3001\u8fd0\u7b97\u80fd\u529b\u548c\u7a7a\u95f4\u60f3\u8c61\u80fd\u529b\uff1b\u80fd\u8fd0\u7528\u57fa\u672c\u6982\u5ff5\u3001\u57fa\u672c\u7406\u8bba\u548c\u57fa\u672c\u65b9\u6cd5\u8fdb\u884c\u63a8\u7406\u3001\u8bc1\u660e\u548c\u8ba1\u7b97\uff1b\u80fd\u8fd0\u7528\u6240\u5b66\u77e5\u8bc6\u5206\u6790\u5e76\u89e3\u51b3\u4e00\u4e9b\u7b80\u5355\u7684\u5b9e\u9645\u95ee\u9898\u3002<\/p>\n
\u8003\u8bd5\u5185\u5bb9
\n\u4e00\u3001\u51fd\u6570\u3001\u6781\u9650\u548c\u8fde\u7eed
\n(\u4e00)\u51fd\u6570
\n1\uff0e\u7406\u89e3\u51fd\u6570\u7684\u6982\u5ff5\uff0c\u4f1a\u6c42\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3001\u8868\u8fbe\u5f0f\u53ca\u51fd\u6570\u503c\uff0c\u4f1a\u4f5c\u51fa\u4e00\u4e9b\u7b80\u5355\u7684\u5206\u6bb5\u51fd\u6570\u56fe\u50cf\u3002
\n2\uff0e\u638c\u63e1\u51fd\u6570\u7684\u5355\u8c03\u6027\u3001\u5947\u5076\u6027\u3001\u6709\u754c\u6027\u548c\u5468\u671f\u6027\u3002
\n3\uff0e\u7406\u89e3\u51fd\u6570y =\u0192(x)\u4e0e\u5176\u53cd\u51fd\u6570y =\u0192-1(x)\u4e4b\u95f4\u7684\u5173\u7cfb(\u5b9a\u4e49\u57df\u3001\u503c\u57df\u3001\u56fe\u50cf)\uff0c\u4f1a\u6c42\u5355\u8c03\u51fd\u6570\u7684\u53cd\u51fd\u6570\u3002
\n4\uff0e\u638c\u63e1\u51fd\u6570\u7684\u56db\u5219\u8fd0\u7b97\u4e0e\u590d\u5408\u8fd0\u7b97; \u638c\u63e1\u590d\u5408\u51fd\u6570\u7684\u590d\u5408\u8fc7\u7a0b\u3002
\n5\uff0e\u638c\u63e1\u57fa\u672c\u521d\u7b49\u51fd\u6570\u7684\u6027\u8d28\u53ca\u5176\u56fe\u50cf\u3002
\n6\uff0e\u7406\u89e3\u521d\u7b49\u51fd\u6570\u7684\u6982\u5ff5\u3002
\n7\uff0e\u4f1a\u5efa\u7acb\u4e00\u4e9b\u7b80\u5355\u5b9e\u9645\u95ee\u9898\u7684\u51fd\u6570\u5173\u7cfb\u5f0f\u3002
\n(\u4e8c)\u6781\u9650
\n1\uff0e\u7406\u89e3\u6781\u9650\u7684\u6982\u5ff5(\u53ea\u8981\u6c42\u6781\u9650\u7684\u63cf\u8ff0\u6027\u5b9a\u4e49)\uff0c\u80fd\u6839\u636e\u6781\u9650\u6982\u5ff5\u63cf\u8ff0\u51fd\u6570\u7684\u53d8\u5316\u8d8b\u52bf\u3002\u7406\u89e3\u51fd\u6570\u5728\u4e00\u70b9\u5904\u6781\u9650\u5b58\u5728\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6\uff0c\u4f1a\u6c42\u51fd\u6570\u5728\u4e00\u70b9\u5904\u7684\u5de6\u6781\u9650\u4e0e\u53f3\u6781\u9650\u3002
\n2\uff0e\u7406\u89e3\u6781\u9650\u7684\u552f\u4e00\u6027\u3001\u6709\u754c\u6027\u548c\u4fdd\u53f7\u6027\uff0c\u638c\u63e1\u6781\u9650\u7684\u56db\u5219\u8fd0\u7b97\u6cd5\u5219\u3002
\n3\uff0e\u7406\u89e3\u65e0\u7a77\u5c0f\u91cf\u3001\u65e0\u7a77\u5927\u91cf\u7684\u6982\u5ff5\uff0c\u638c\u63e1\u65e0\u7a77\u5c0f\u91cf\u7684\u6027\u8d28\uff0c\u65e0\u7a77\u5c0f\u91cf\u4e0e\u65e0\u7a77\u5927\u91cf\u7684\u5173\u7cfb\u3002\u4f1a\u6bd4\u8f83\u65e0\u7a77\u5c0f\u91cf\u7684\u9636(\u9ad8\u9636\u3001\u4f4e\u9636\u3001\u540c\u9636\u548c\u7b49\u4ef7)\u3002\u4f1a\u8fd0\u7528\u7b49\u4ef7\u65e0\u7a77\u5c0f\u91cf\u66ff\u6362\u6c42\u6781\u9650\u3002
\n4\uff0e\u7406\u89e3\u6781\u9650\u5b58\u5728\u7684\u4e24\u4e2a\u6536\u655b\u51c6\u5219(\u5939\u903c\u51c6\u5219\u4e0e\u5355\u8c03\u6709\u754c\u51c6\u5219)\uff0c\u638c\u63e1\u4e24\u4e2a\u91cd\u8981\u6781\u9650\uff1a
\n\uff0c\uff0c
\n\u5e76\u80fd\u7528\u8fd9\u4e24\u4e2a\u91cd\u8981\u6781\u9650\u6c42\u51fd\u6570\u7684\u6781\u9650\u3002
\n(\u4e09)\u8fde\u7eed
\n1\uff0e\u7406\u89e3\u51fd\u6570\u5728\u4e00\u70b9\u5904\u8fde\u7eed\u7684\u6982\u5ff5\uff0c\u51fd\u6570\u5728\u4e00\u70b9\u5904\u8fde\u7eed\u4e0e\u51fd\u6570\u5728\u8be5\u70b9\u5904\u6781\u9650\u5b58\u5728\u7684\u5173\u7cfb\u3002\u4f1a\u5224\u65ad\u5206\u6bb5\u51fd\u6570\u5728\u5206\u6bb5\u70b9\u7684\u8fde\u7eed\u6027\u3002
\n2\uff0e\u7406\u89e3\u51fd\u6570\u5728\u4e00\u70b9\u5904\u95f4\u65ad\u7684\u6982\u5ff5\uff0c\u4f1a\u6c42\u51fd\u6570\u7684\u95f4\u65ad\u70b9\uff0c\u5e76\u4f1a\u5224\u65ad\u95f4\u65ad\u70b9\u7684\u7c7b\u578b\u3002
\n3\uff0e\u7406\u89e3\u201c\u4e00\u5207\u521d\u7b49\u51fd\u6570\u5728\u5176\u5b9a\u4e49\u533a\u95f4\u4e0a\u90fd\u662f\u8fde\u7eed\u7684\u201d\uff0c\u5e76\u4f1a\u5229\u7528\u521d\u7b49\u51fd\u6570\u7684\u8fde\u7eed\u6027\u6c42\u51fd\u6570\u7684\u6781\u9650\u3002
\n4\uff0e\u638c\u63e1\u95ed\u533a\u95f4\u4e0a\u8fde\u7eed\u51fd\u6570\u7684\u6027\u8d28\uff1a\u6700\u503c\u5b9a\u7406(\u6709\u754c\u6027\u5b9a\u7406)\uff0c\u4ecb\u503c\u5b9a\u7406(\u96f6\u70b9\u5b58\u5728\u5b9a\u7406)\u3002\u4f1a\u8fd0\u7528\u4ecb\u503c\u5b9a\u7406\u63a8\u8bc1\u4e00\u4e9b\u7b80\u5355\u547d\u9898\u3002<\/p>\n
\u4e8c\u3001\u4e00\u5143\u51fd\u6570\u5fae\u5206\u5b66
\n(\u4e00)\u5bfc\u6570\u4e0e\u5fae\u5206
\n1\uff0e\u7406\u89e3\u5bfc\u6570\u7684\u6982\u5ff5\u53ca\u5176\u51e0\u4f55\u610f\u4e49\uff0c\u4e86\u89e3\u5de6\u5bfc\u6570\u4e0e\u53f3\u5bfc\u6570\u7684\u5b9a\u4e49\uff0c\u7406\u89e3\u51fd\u6570\u7684\u53ef\u5bfc\u6027\u4e0e\u8fde\u7eed\u6027\u7684\u5173\u7cfb\uff0c\u4f1a\u7528\u5b9a\u4e49\u6c42\u51fd\u6570\u5728\u4e00\u70b9\u5904\u7684\u5bfc\u6570\u3002
\n2\uff0e\u4f1a\u6c42\u66f2\u7ebf\u4e0a\u4e00\u70b9\u5904\u7684\u5207\u7ebf\u65b9\u7a0b\u4e0e\u6cd5\u7ebf\u65b9\u7a0b\u3002
\n3\uff0e\u719f\u8bb0\u5bfc\u6570\u7684\u57fa\u672c\u516c\u5f0f\uff0c\u4f1a\u8fd0\u7528\u51fd\u6570\u7684\u56db\u5219\u8fd0\u7b97\u6c42\u5bfc\u6cd5\u5219\uff0c\u590d\u5408\u51fd\u6570\u6c42\u5bfc\u6cd5\u5219\u548c\u53cd\u51fd\u6570\u6c42\u5bfc\u6cd5\u5219\u6c42\u5bfc\u6570\u3002\u4f1a\u6c42\u5206\u6bb5\u51fd\u6570\u7684\u5bfc\u6570\u3002
\n4\uff0e\u4f1a\u6c42\u9690\u51fd\u6570\u7684\u5bfc\u6570\u3002\u638c\u63e1\u5bf9\u6570\u6c42\u5bfc\u6cd5\u4e0e\u53c2\u6570\u65b9\u7a0b\u6c42\u5bfc\u6cd5\u3002
\n5\uff0e\u7406\u89e3\u9ad8\u9636\u5bfc\u6570\u7684\u6982\u5ff5\uff0c\u4f1a\u6c42\u4e00\u4e9b\u7b80\u5355\u7684\u51fd\u6570\u7684n\u9636\u5bfc\u6570\u3002
\n6\uff0e\u7406\u89e3\u51fd\u6570\u5fae\u5206\u7684\u6982\u5ff5\uff0c\u638c\u63e1\u5fae\u5206\u8fd0\u7b97\u6cd5\u5219\u4e0e\u4e00\u9636\u5fae\u5206\u5f62\u5f0f\u4e0d\u53d8\u6027\uff0c\u7406\u89e3\u53ef\u5fae\u4e0e\u53ef\u5bfc\u7684\u5173\u7cfb\uff0c\u4f1a\u6c42\u51fd\u6570\u7684\u4e00\u9636\u5fae\u5206\u3002
\n(\u4e8c)\u4e2d\u503c\u5b9a\u7406\u53ca\u5bfc\u6570\u7684\u5e94\u7528
\n1\uff0e\u7406\u89e3\u7f57\u5c14(Rolle)\u4e2d\u503c\u5b9a\u7406\u3001\u62c9\u683c\u6717\u65e5(Lagrange)\u4e2d\u503c\u5b9a\u7406\u53ca\u5b83\u4eec\u7684\u51e0\u4f55\u610f\u4e49\uff0c\u7406\u89e3\u67ef\u897f(Cauchy)\u4e2d\u503c\u5b9a\u7406\u3001\u6cf0\u52d2(Taylor)\u4e2d\u503c\u5b9a\u7406\u3002\u4f1a\u7528\u7f57\u5c14\u4e2d\u503c\u5b9a\u7406\u8bc1\u660e\u65b9\u7a0b\u6839\u7684\u5b58\u5728\u6027\u3002\u4f1a\u7528\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u5b9a\u7406\u8bc1\u660e\u4e00\u4e9b\u7b80\u5355\u7684\u4e0d\u7b49\u5f0f\u3002
\n2\uff0e\u638c\u63e1\u6d1b\u5fc5\u8fbe(L\u2019Hospital)\u6cd5\u5219\uff0c\u4f1a\u7528\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u6c42\u201c\u201d\uff0c\u201c\u201d\uff0c\u201c\u201d\uff0c\u201c\u201d\uff0c\u201c\u201d\uff0c\u201c\u201d\u548c\u201c\u201d\u578b\u672a\u5b9a\u5f0f\u7684\u6781\u9650\u3002
\n3\uff0e\u4f1a\u5229\u7528\u5bfc\u6570\u5224\u5b9a\u51fd\u6570\u7684\u5355\u8c03\u6027\uff0c\u4f1a\u6c42\u51fd\u6570\u7684\u5355\u8c03\u533a\u95f4\uff0c\u4f1a\u5229\u7528\u51fd\u6570\u7684\u5355\u8c03\u6027\u8bc1\u660e\u4e00\u4e9b\u7b80\u5355\u7684\u4e0d\u7b49\u5f0f\u3002
\n4\uff0e\u7406\u89e3\u51fd\u6570\u6781\u503c\u7684\u6982\u5ff5\uff0c\u4f1a\u6c42\u51fd\u6570\u7684\u6781\u503c\u548c\u6700\u503c\uff0c\u4f1a\u89e3\u51b3\u4e00\u4e9b\u7b80\u5355\u7684\u5e94\u7528\u95ee\u9898\u3002
\n5\uff0e\u4f1a\u5224\u5b9a\u66f2\u7ebf\u7684\u51f9\u51f8\u6027\uff0c\u4f1a\u6c42\u66f2\u7ebf\u7684\u62d0\u70b9\u3002
\n6\uff0e\u4f1a\u6c42\u66f2\u7ebf\u7684\u6e10\u8fd1\u7ebf(\u6c34\u5e73\u6e10\u8fd1\u7ebf\u3001\u5782\u76f4\u6e10\u8fd1\u7ebf\u548c\u659c\u6e10\u8fd1\u7ebf)\u3002
\n7\uff0e\u4f1a\u63cf\u7ed8\u4e00\u4e9b\u7b80\u5355\u7684\u51fd\u6570\u7684\u56fe\u5f62\u3002<\/p>\n
\u4e09\u3001\u4e00\u5143\u51fd\u6570\u79ef\u5206\u5b66
\n(\u4e00)\u4e0d\u5b9a\u79ef\u5206
\n1\uff0e\u7406\u89e3\u539f\u51fd\u6570\u4e0e\u4e0d\u5b9a\u79ef\u5206\u7684\u6982\u5ff5\u53ca\u5176\u5173\u7cfb\uff0c\u7406\u89e3\u539f\u51fd\u6570\u5b58\u5728\u5b9a\u7406\uff0c\u638c\u63e1\u4e0d\u5b9a\u79ef\u5206\u7684\u6027\u8d28\u3002
\n2\uff0e\u719f\u8bb0\u57fa\u672c\u4e0d\u5b9a\u79ef\u5206\u516c\u5f0f\u3002
\n3\uff0e\u638c\u63e1\u4e0d\u5b9a\u79ef\u5206\u7684\u7b2c\u4e00\u7c7b\u6362\u5143\u6cd5(\u201c\u51d1\u201d\u5fae\u5206\u6cd5)\uff0c\u7b2c\u4e8c\u7c7b\u6362\u5143\u6cd5(\u9650\u4e8e\u4e09\u89d2\u6362\u5143\u4e0e\u4e00\u4e9b\u7b80\u5355\u7684\u6839\u5f0f\u6362\u5143)\u3002
\n4\uff0e\u638c\u63e1\u4e0d\u5b9a\u79ef\u5206\u7684\u5206\u90e8\u79ef\u5206\u6cd5\u3002
\n5\uff0e\u4f1a\u6c42\u4e00\u4e9b\u7b80\u5355\u7684\u6709\u7406\u51fd\u6570\u7684\u4e0d\u5b9a\u79ef\u5206\u3002
\n(\u4e8c)\u5b9a\u79ef\u5206
\n1\uff0e\u7406\u89e3\u5b9a\u79ef\u5206\u7684\u6982\u5ff5\u4e0e\u51e0\u4f55\u610f\u4e49, \u638c\u63e1\u5b9a\u79ef\u5206\u7684\u57fa\u672c\u6027\u8d28\u3002
\n2\uff0e\u7406\u89e3\u53d8\u9650\u79ef\u5206\u51fd\u6570\u7684\u6982\u5ff5\uff0c\u638c\u63e1\u53d8\u9650\u79ef\u5206\u51fd\u6570\u6c42\u5bfc\u7684\u65b9\u6cd5\u3002
\n3\uff0e\u638c\u63e1\u725b\u987f\u2014\u83b1\u5e03\u5c3c\u8328(Newton\u2014Leibniz)\u516c\u5f0f\u3002
\n4\uff0e\u638c\u63e1\u5b9a\u79ef\u5206\u7684\u6362\u5143\u79ef\u5206\u6cd5\u4e0e\u5206\u90e8\u79ef\u5206\u6cd5\u3002
\n5\uff0e\u7406\u89e3\u65e0\u7a77\u533a\u95f4\u4e0a\u6709\u754c\u51fd\u6570\u7684\u5e7f\u4e49\u79ef\u5206\u4e0e\u6709\u9650\u533a\u95f4\u4e0a\u65e0\u754c\u51fd\u6570\u7684\u7455\u79ef\u5206\u7684\u6982\u5ff5\uff0c\u638c\u63e1\u5176\u8ba1\u7b97\u65b9\u6cd5\u3002
\n6\uff0e\u4f1a\u7528\u5b9a\u79ef\u5206\u8ba1\u7b97\u5e73\u9762\u56fe\u5f62\u7684\u9762\u79ef\u4ee5\u53ca\u5e73\u9762\u56fe\u5f62\u7ed5\u5750\u6807\u8f74\u65cb\u8f6c\u4e00\u5468\u6240\u5f97\u7684\u65cb\u8f6c\u4f53\u7684\u4f53\u79ef\u3002<\/p>\n
\u56db\u3001\u65e0\u7a77\u7ea7\u6570
\n(\u4e00)\u6570\u9879\u7ea7\u6570
\n1\uff0e\u7406\u89e3\u7ea7\u6570\u6536\u655b\u3001\u7ea7\u6570\u53d1\u6563\u7684\u6982\u5ff5\u548c\u7ea7\u6570\u7684\u57fa\u672c\u6027\u8d28\uff0c\u638c\u63e1\u7ea7\u6570\u6536\u655b\u7684\u5fc5\u8981\u6761\u4ef6\u3002
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\n\u51fd\u6570\u3001\u6781\u9650\u548c\u8fde\u7eed \u7ea620%
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\n\u4e00\u5143\u51fd\u6570\u79ef\u5206\u5b66 \u7ea630%
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