{"id":1322,"date":"2024-03-29T17:38:00","date_gmt":"2024-03-29T09:38:00","guid":{"rendered":"http:\/\/jiaohuweike.online\/?p=1322"},"modified":"2025-09-23T22:28:51","modified_gmt":"2025-09-23T14:28:51","slug":"daoshuqiexian4","status":"publish","type":"post","link":"http:\/\/jhwk.online\/?p=1322","title":{"rendered":"\u5bfc\u6570\u7814\u7a76\u5207\u7ebf\u95ee\u9898"},"content":{"rendered":"\n<div class=\"wp-block-stackable-spacer stk-block-spacer stk--no-padding stk-block stk-711932c\" data-block-id=\"711932c\"><\/div>\n\n\n\n<div class=\"wp-block-ht-block-toc  is-style-outline htoc htoc--position-wide toc-list-style-plain\" data-htoc-state=\"expanded\" data-htoc-scrollspy=\"false\"><span class=\"htoc__title\"><span class=\"ht_toc_title\">\u76ee\u5f55<\/span><span class=\"htoc__toggle\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\"><g fill=\"#444\"><path d=\"M15 7H1c-.6 0-1 .4-1 1s.4 1 1 1h14c.6 0 1-.4 1-1s-.4-1-1-1z\"><\/path><path d=\"M15 1H1c-.6 0-1 .4-1 1s.4 1 1 1h14c.6 0 1-.4 1-1s-.4-1-1-1zM15 13H1c-.6 0-1 .4-1 1s.4 1 1 1h14c.6 0 1-.4 1-1s-.4-1-1-1z\"><\/path><\/g><\/svg><\/span><\/span><div class=\"htoc__itemswrap\"><ul class=\"ht_toc_list\"><li class=\"\"><a href=\"#htoc-\">\u5728\uff08\u8fc7\uff09\u67d0\u70b9\u7684\u5207\u7ebf<\/a><\/li><li class=\"\"><a href=\"#htoc-1111\">\u4e24\u6761\u66f2\u7ebf\u7684\u516c\u5207\u7ebf<\/a><\/li><\/ul><\/div><\/div>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"htoc-\">\u5728\uff08\u8fc7\uff09\u67d0\u70b9\u7684\u5207\u7ebf<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>1.\u5df2\u77e5\u51fd\u6570f(x)=x^3+x-16,\u6c42\u66f2\u7ebfy=f(x)\u5728\u70b9(2,-6)\u5904\u7684\u5207\u7ebf\u65b9\u7a0b.~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p class=\"wp-block-paragraph\" id=\"htoc-1\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-y-13x-32\"><pre>\u7b54\u6848\uff1ay=13x-32~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>2.\u5df2\u77e5\u51fd\u6570f(x)=x^3+x-16,\u8fc7\u539f\u70b9\u4f5c\u66f2\u7ebff(x)\u7684\u5207\u7ebf\uff0c\u6c42\u5207\u7ebf\u65b9\u7a0b\u3002~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p class=\"wp-block-paragraph\" id=\"htoc-11\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-y-13x\"><pre>\u7b54\u6848\uff1ay=13x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>3.\u5df2\u77e5\u66f2\u7ebff(x)=x^3+ax+\\frac{1}{4}\u5728\u70b9x=0\u5904\u7684\u5207\u7ebf\u4e0e\u66f2\u7ebfg(x)=-lnx\u76f8\u5207\uff0c~~~~~~~~~~~~~~~~\\\\\u6c42a\u7684\u503c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p class=\"wp-block-paragraph\" id=\"htoc-111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-a-e-frac-3-4\"><pre>\u7b54\u6848\uff1aa=-e^{-\\frac{3}{4}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-f64e97d\" data-block-id=\"f64e97d\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-c7fbf8f\" data-block-id=\"c7fbf8f\"><style>.stk-c7fbf8f .stk-button{border-top-left-radius:11px !important;border-top-right-radius:11px !important;border-bottom-right-radius:11px !important;border-bottom-left-radius:11px !important;}.stk-c7fbf8f .stk-button:before{box-shadow:0 0 0 2px #7878781a !important;}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"\/fabu\/%E5%AF%BC%E6%95%B0%E8%A7%A3%E5%86%B3%E5%88%87%E7%BA%BF%E9%97%AE%E9%A2%981-3\/HTML5\/test.html\" target=\"_blank\" rel=\"noreferrer noopener\"><span class=\"stk-button__inner-text\">\u89c2\u770b\u5fae\u8bfe<\/span><\/a><\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"htoc-1111\">\u4e24\u6761\u66f2\u7ebf\u7684\u516c\u5207\u7ebf<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>4.\u6c42\u66f2\u7ebfy=lnx+2\u548c\u66f2\u7ebfy=ln(x+1)\u7684\u516c\u5207\u7ebf\u3002~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p class=\"wp-block-paragraph\" id=\"htoc-11111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-y-2x-1-ln-2\"><pre>\u7b54\u6848\uff1ay=2x+1-\\ln 2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>5.\u82e5\u4e00\u76f4\u7ebf\u4e0e\u66f2\u7ebfy=elnx\u548c\u66f2\u7ebfy=mx^2\u76f8\u5207\u4e0e\u540c\u4e00\u70b9P,\u6c42\u5b9e\u6570m\u7684\u503c\u3002 ~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p class=\"wp-block-paragraph\" id=\"htoc-111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-m-frac-1-2\"><pre>\u7b54\u6848\uff1am=\\frac{1}{2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-stackable-spacer stk-block-spacer stk--no-padding stk-block stk-1dda9ec\" data-block-id=\"1dda9ec\"><style>.stk-1dda9ec {height:30px !important;}<\/style><\/div>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-38fe971\" data-block-id=\"38fe971\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-cd579de\" data-block-id=\"cd579de\"><style>.stk-cd579de .stk-button{border-top-left-radius:11px !important;border-top-right-radius:11px !important;border-bottom-right-radius:11px !important;border-bottom-left-radius:11px !important;}.stk-cd579de .stk-button:before{box-shadow:0 0 0 2px #7878781a !important;}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"\/fabu\/%E5%AF%BC%E6%95%B0%E8%A7%A3%E5%86%B3%E5%88%87%E7%BA%BF%E9%97%AE%E9%A2%984-5\/HTML5\/test.html\" target=\"_blank\" rel=\"noreferrer noopener\"><span class=\"stk-button__inner-text\">\u89c2\u770b\u5fae\u8bfe<\/span><\/a><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-spacer stk-block-spacer stk--no-padding stk-block stk-23cb53d\" data-block-id=\"23cb53d\"><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>6.\u82e5\u66f2\u7ebf  y=(x+a) \\mathrm{e}^{x}  \u6709\u4e24\u6761\u8fc7\u5750\u6807\u539f\u70b9\u7684\u5207\u7ebf,\u6c42  a  \u7684\u53d6\u503c\u8303\u56f4.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p class=\"wp-block-paragraph\" id=\"htoc-1111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-infty-4-cup-0-infty-y-left-x-0-a-right-mathrm-e-x-0-left-mathrm-e-x-0-left-x-0-a-right-mathrm-e-x-0-right-left-x-x-0-right-rightarrow-left-x-0-a-right-mathrm-e-x-0-left-mathrm-e-x-0-left-x-0-a-right-mathrm-e-x-0-right-left-x-0-right-x-2-a-x-0-a-0-delta-a-2-4-a-gt-0-a-lt-4-a-gt-0\"><pre>\u7b54\u6848:(-\\infty,-4) \\cup(0,+\\infty) ;\u63d0\u793a\uff1ay-\\left(x_{0}+a\\right) \\mathrm{e}^{x_{0}}=\\left[\\mathrm{e}^{x_{0}}+\\left(x_{0}+a\\right) \\mathrm{e}^{x_{0}}\\right]\\left(x-x_{0}\\right)~~~~~~~~~\\\\\u4e3a\u5207\u7ebf\u65b9\u7a0b\uff0c\u8fc7\u539f\u70b9,\n\\Rightarrow  -\\left(x_{0}+a\\right) \\mathrm{e}^{x_{0}}=\\left[\\mathrm{e}^{x_{0}}+\\left(x_{0}+a\\right) \\mathrm{e}^{x_{0}}\\right]\\left(-x_{0}\\right) ,\n\u6574\u7406\u5f97:~~~~~~~~~~~~~~~~~\\\\  x^{2}+a x_{0}-a=0  \u3002\n\u6709\u4e24\u4e2a\u4e0d\u540c\u7684\u6839,\n\u6240\u4ee5  \\Delta=a^{2}+4 a&gt;0 , \u89e3\u5f97  a&lt;-4  \u6216  a&gt;0 ~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>7.\u82e5\u8fc7  y  \u8f74\u4e0a\u4e00\u70b9  P(0, m)  \u53ef\u4f5c\u51fa  3 \u6761\u76f4\u7ebf\u4e0e\u51fd\u6570  f(x)=x \\mathrm{e}^{x}  \u7684\u56fe\u8c61\u76f8\u5207,\u6c42m\u7684\u8303\u56f4.~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p class=\"wp-block-paragraph\" id=\"htoc-11111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-m-in-4e-2-0-m-x-2e-x\"><pre>\u7b54\u6848\uff1am\\in(-4e^{-2},0);\u63d0\u793a\uff1a\u8f6c\u5316\u4e3a-m=x^2e^{x}\u6709\u4e09\u4e2a\u4ea4\u70b9\u95ee\u9898.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>8.\u5df2\u77e5\u51fd\u6570f(x)=e^{x}\u4e0e\u51fd\u6570g(x)=lnx+b\u5b58\u5728\u4e00\u6761\u8fc7\u539f\u70b9\u7684\u516c\u5171\u5207\u7ebf\uff0c\u6c42b\u7684\u503c.~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p class=\"wp-block-paragraph\" id=\"htoc-111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-b-2-y-e-x-y-ex-g-x-therefore-g-x-frac-1-x-e-rightarrow-g-x-frac-1-e-1-rightarrow-b-2\"><pre>\u7b54\u6848\uff1ab=2\uff1b\u63d0\u793a\uff1a\u5148\u6c42y=e^x\u8fc7\u539f\u70b9\u7684\u5207\u7ebf\u4e3ay=ex,\u4e5f\u662fg(x)\u7684\u5207\u7ebf\uff0c\\therefore g'(x)=~~\\\\ \\frac{1}{x}=e,\\Rightarrow g(x)\u5207\u70b9\u4e3a(\\frac{1}{e},1),\\Rightarrow b=2.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u53d8\u5f0f\uff1a\u76f4\u7ebfy=kx\u662f\u66f2\u7ebff(x)=\\ln x \u7684\u5207\u7ebf\uff0c\u4e5f\u662f\u66f2\u7ebfg(x)=ae^x\u7684\u5207\u7ebf\uff0c\u6c42a\u7684\u503c.~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p class=\"wp-block-paragraph\" id=\"htoc-1111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-a-frac-1-e-2-y-kx-k-frac-1-e\"><pre>\u7b54\u6848\uff1aa=\\frac{1}{e^2};\u63d0\u793a\uff1ay=kx\u662f\u8fc7\u539f\u70b9\u7684\u76f4\u7ebf\uff0ck=\\frac{1}{e}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>9.\u5df2\u77e5  f(x)=\\mathrm{e}^{x}, g(x)=\\ln x+2 , \u76f4\u7ebf  l  \u662f  f(x)  \u4e0e  g(x)  \u7684\u516c\u5207\u7ebf, \u6c42\u76f4\u7ebf  l  \u7684\u65b9\u7a0b.~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p class=\"wp-block-paragraph\" id=\"htoc-11111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-y-mathrm-e-x-y-x-1-1-y-mathrm-e-x-1-mathrm-e-x-1-left-x-x-1-right-2-y-frac-1-x-2-cdot-x-ln-x-2-1-x-1-1-x-1-0-l-y-mathrm-e-x-y-x-1\"><pre>\u7b54\u6848\uff1a y=\\mathrm{e} x  \u6216  y=x+1 \uff1b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\u63d0\u793a\uff1a\u5207\u7ebf 1:  y-\\mathrm{e}^{x_{1}}=\\mathrm{e}^{x_{1}}\\left(x-x_{1}\\right) ,\n\n\u5207\u7ebf 2:  y=\\frac{1}{x_{2}} \\cdot x+\\ln x_{2}+1 ,\u4e24\u5f0f\u5bf9\u5e94\u7cfb\u6570~~~~~~~\\\\\u76f8\u540c\u5f97\uff0cx_{1}=1  \u6216  x_{1}=0 ,\u6240\u4ee5\uff0c\u76f4\u7ebf  l  \u7684\u65b9\u7a0b\u4e3a  y=\\mathrm{e} x  \u6216  y=x+1 .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n","protected":false},"excerpt":{"rendered":"<p>\u4e24\u6761\u66f2\u7ebf\u7684\u516c\u5207\u7ebf<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[23],"class_list":["post-1322","post","type-post","status-publish","format-standard","hentry","category-4","tag-23"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1322","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1322"}],"version-history":[{"count":1,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1322\/revisions"}],"predecessor-version":[{"id":4141,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1322\/revisions\/4141"}],"wp:attachment":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1322"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1322"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1322"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}