{"id":1580,"date":"2024-04-23T18:01:12","date_gmt":"2024-04-23T10:01:12","guid":{"rendered":"http:\/\/jiaohuweike.online\/?p=1580"},"modified":"2024-04-23T18:01:12","modified_gmt":"2024-04-23T10:01:12","slug":"hsyldwt-5-3-4-4","status":"publish","type":"post","link":"http:\/\/jhwk.online\/?p=1580","title":{"rendered":"\u5bfc\u6570\u7efc\u5408\u9898-\u63d0\u9ad8\u7bc7"},"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-stackable-heading stk-block-heading stk-block-heading--v2 stk-block stk-fa21366\" id=\"\u51fd\u6570\u7684\u9690\u96f6\u70b9\u95ee\u9898\" data-block-id=\"fa21366\"><h4 class=\"stk-block-heading__text\">\u51fd\u6570\u7684\u9690\u96f6\u70b9\u95ee\u9898<\/h4><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>1.\u51fd\u6570f(x)=e^x-ln(x+m),\u5f53m&lt;2\u65f6\uff0c\u6c42\u8bc1f(x)&gt;0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-d0024a5\" data-block-id=\"d0024a5\"><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-c4528ea\" data-block-id=\"c4528ea\"><style>.stk-c4528ea .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-c4528ea .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%E7%BB%BC%E5%90%88%E9%A2%98%E6%8F%90%E9%AB%98%E7%AF%871\/HTML5\/practice.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-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7ec3\u4e60\uff1a\u5df2\u77e5\u51fd\u6570f(x)=-x+\\ln x+1,g(x)=xe^x-2x,\u6c42\u8bc1\uff1af(x)\\le g(x).~~~~~~~~~~~~~~~~~~~<\/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 \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\exists x_0\\in (\\frac{1}{2},1),\\frac{1}{x_0}=e^{x_0},\\therefore  x_0e^{x_0}=1,-\\ln x_0=x_0.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\\therefore F(x)\\le F(x_0)=\\ln x_0+1-x_0e^{x_0}+x_0=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\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\">\u53cc\u53d8\u91cf\u95ee\u9898<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>2.\u5df2\u77e5\u51fd\u6570f(x)=mx\\ln x+x^2,m\\ne 0.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\(1)\u82e5m=-2,\u6c42\u51fd\u6570f(x)\u7684\u5355\u8c03\u533a\u95f4\uff1b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\(2)\u82e5f(x_1)=f(x_2)=0,\u4e14x_1\\ne x_2,\u8bc1\u660e\uff1a\\ln x_1+\\ln x_2&gt;2.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-3095f64\" data-block-id=\"3095f64\"><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-69e0dc5\" data-block-id=\"69e0dc5\"><style>.stk-69e0dc5 .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-69e0dc5 .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%E7%BB%BC%E5%90%88%E9%A2%98%E2%80%94%E2%80%94%E6%8F%90%E9%AB%98%E7%AF%872\/HTML5\/practice.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-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u53d8\u5f0f\uff1a\u5df2\u77e5\u51fd\u6570  f(x)=\\ln x-a x(x&gt;0), a  \u4e3a\u5e38\u6570, \u82e5\u51fd\u6570  f(x)  \u6709\u4e24\u4e2a\u96f6\u70b9  x_{1}, x_{2}~~~~~~~~~~~~\\\\\\left(x_{1} \\neq x_{2}\\right) ,\n\u6c42\u8bc1:  x_{1} x_{2}&gt;\\mathrm{e}^{2} .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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 \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u63d0\u793a\uff1a\u8bbe\u4e24\u96f6\u70b9x_{1}&gt;x_{2}&gt;0,\\left\\{\\begin{matrix}\n \\ln x_1=ax_1 &amp; \\\\\n\\ln x_2=ax_2  &amp;\n\\end{matrix}\\right.\\Rightarrow \\left\\{\\begin{matrix}\n \\ln x_{1}+\\ln x_{2}=a\\left(x_{1}+x_{2}\\right) &amp; \\\\\n \\ln x_{1}-\\ln x_{2}=a\\left(x_{1}-x_{2}\\right) &amp;\n\\end{matrix}\\right.\\Rightarrow~~~~~~~~\\\\\\frac{\\ln x_{1}+\\ln x_{2}}{\\ln x_{1}-\\ln x_{2}} =\\frac{x_1+x_2}{x_1-x_2} \\Rightarrow\\frac{\\ln x_1x_2}{\\ln \\frac{x_1}{x_2}}=\\frac{\\frac{x_1}{x_2}+1}{\\frac{x_1}{x_2}-1},\\Rightarrow \\ln x_1x_2=\\frac{\\frac{x_1}{x_2}+1}{\\frac{x_1}{x_2}-1}\\cdot\\ln \\frac{x_1}{x_2} ,\u7531x_1x_2&gt;e^2,\\\\\\ln x_1x_2&gt;2,\u4ee4  t=\\frac{x_{1}}{x_{2}}(t&gt;1) ,\n\u5219\u4e0d\u7b49\u5f0f\u53d8\u4e3a  \\ln t&gt;\\frac{2(t-1)}{t+1} .\n\u4ee4  h(t)=\\ln t-\\frac{2(t-1)}{t+1} ,~~~~~\\\\\n\nh(t)&gt;h(1)=\\ln 1-0=0.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\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\">\u51fd\u6570\u7684\u9690\u96f6\u70b9\u95ee\u9898\uff0c\u540c\u6784<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>3.\u5df2\u77e5\u51fd\u6570f(x)=xe^x-\\ln x-1,\u82e5f(x)\\ge mx\u6052\u6210\u7acb\uff0c\u6c42\u5b9e\u6570m\u7684\u53d6\u503c\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 \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>m\\le1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-7cb73da\" data-block-id=\"7cb73da\"><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-f52db75\" data-block-id=\"f52db75\"><style>.stk-f52db75 .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-f52db75 .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%E7%BB%BC%E5%90%88%E9%A2%98%E2%80%94%E2%80%94%E6%8F%90%E9%AB%98%E7%AF%873\/HTML5\/practice.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-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7ec3\u4e601.\u82e5\u5173\u4e8ex\u7684\u65b9\u7a0bm+e\\ln m=\\frac{x}{e^x}+e(\\ln x-x)\u6709\u89e3\uff0c\u6c42m\u7684\u6700\u5927\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 \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7b54\u6848:\\frac{1}{e};\u63d0\u793a\uff1a\u5de6=m+e\\ln m=e^{\\ln m}+e\\ln m;\u53f3=\\frac{e^{\\ln x}}{e^x}+e(\\ln x-x)=~~~~~~~~~~~~~~~~~~~\\\\e^{\\ln x-x}+e(\\ln x-x),\\therefore \\ln m=\\ln x-x,\\therefore\\ln m\\le-1,\\therefore m\\le\\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>\u7ec3\u4e602\uff1a\u5df2\u77e5\u51fd\u6570  f(x)=e^{2 a x}-3 \\ln x , \u82e5  f(x)&gt;x^{3}-2 a x  \u6052\u6210\u7acb, \u5219\u5b9e\u6570  a  \u7684\u53d6\u503c\u8303\u56f4~~~\\\\\u4e3a  (~~~~  )~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\nA.  \\left(0, \\frac{3}{2 e}\\right) ~~~~\nB.  \\left(\\frac{3}{2 e},+\\infty\\right) ~~~~\nC.  \\left(0, \\frac{3}{e}\\right) ~~~~\nD.  \\left(\\frac{3}{e},+\\infty\\right) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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 \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7b54\u6848\uff1aB\uff1b\u63d0\u793a\uff1af(x)=e^{2 a x}-3 \\ln x&gt;x^3-2ax,\\therefore e^{2 a x}+2ax&gt;x^3+\\ln x^3,~~~~~~~~~~~~~~~~\\\\\\because x^3=e^{\\ln x^3},\\therefore e^{2 a x}+2ax&gt;e^{\\ln x^3}+\\ln x^3(\u540c\u6784)\uff0cy=e^t+t\u5355\u589e\uff0c\\therefore2ax&gt;\\ln x^3,~~~~~~~\\\\\\therefore 2a&gt;\\frac{3\\ln x}{x},a&gt;\\frac{3}{2e}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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>\u7ec3\u4e603.\u82e5\u4e0d\u7b49\u5f0fae^{2x}+x+\\ln a\\ge\\ln x\u5bf9\u4efb\u610fx\\in (0,+\\infty)\u6210\u7acb\uff0c\u6c42\u5b9e\u6570a \u7684\u53d6\u503c\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 \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7b54\u6848\uff1aa\\ge\\frac{1}{2e}\uff1b\u63d0\u793a\uff1a\u5de6=e^{\\ln a}e^{2x}+x+\\ln a=e^{2x+\\ln a}+x+\\ln a\\ge \\ln x,\u4e24\u8fb9\u52a0x~~~~~~\\\\\u5f97\uff0ce^{2x+\\ln a}+2x+\\ln a\\ge x+\\ln x=e^{\\ln x}+\\ln x,\u6784\u9020\u51fd\u6570y=e^x+x,\u5355\u589e,~~~~~~~~~~~~~~~~~~~\\\\\\therefore2x+\\ln a\\ge\\ln x,\\therefore \\ln a\\ge\\ln x-2x,a\\ge\\frac{1}{2e}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\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\">\u53c2\u6570\u8303\u56f4\u3001 \u6d1b\u5fc5\u8fbe\u6cd5\u5219<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>4.\u5df2\u77e5\u51fd\u6570f(x)=m\\ln x-2x^2(m\\in R).\u82e5\u5bf9\\forall x\\in (1,+\\infty),\u4e0d\u7b49\u5f0ff(x)&lt;-2\u6052\u6210\u7acb\uff0c\\\\\u6c42\u5b9e\u6570m\u7684\u53d6\u503c\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 \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>m\\le4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-863cbc9\" data-block-id=\"863cbc9\"><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-7297e34\" data-block-id=\"7297e34\"><style>.stk-7297e34 .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-7297e34 .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%E7%BB%BC%E5%90%88%E9%A2%98%E2%80%94%E2%80%94%E6%8F%90%E9%AB%98%E7%AF%874\/HTML5\/practice.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-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7ec3\u4e601\uff1a\u5df2\u77e5e^x+\\sin x\\ge ax+1\u5bf9\u4efb\u610fx\\in [0,+\\infty)\u6052\u6210\u7acb\uff0c\u6c42\u5b9e\u6570a\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\uff1a<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7b54\u6848\uff1aa\\le 2;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n\u63d0\u793a\uff1a\u6cd5\u4e00\u3001\u5206\u79bb\u53c2\u91cf\u3002\u5f53  x=0  \u65f6,  \u663e\u7136\u6210\u7acb;\u5f53x>0\u65f6\uff0c\na\\le \\frac{e^x+\\sin x -1}{x}=f(x),\\\\\u53ea\u9700\u6c42f(x)_{min}, f^{\\prime}(x)=   \\frac{(x-1) e^{x}+x \\cos x-\\sin x+1}{x^{2}} , \u4ee4\u5206\u5b50\u4e3a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n g(x)=(x-1) e^{x}+x \\cos x-\\sin x+1 , \u4e0b\u9762\u5224\u65adg(x)\u7684\u6b63\u8d1f\uff0c\u89c2\u5bdf\u7aef\u70b9\u503cg(0)=0,\u53c8 ~~\\\\ g^{\\prime}   (x)=x e^{x}-x \\sin x=x\\left(e^{x}-\\sin x\\right) , \u56e0\u4e3a  x>0 ,\u6240\u4ee5 \u6240\u4ee5  g^{\\prime}(x)>0 , \u6240\u4ee5  g(x)  \u5728~~~~~~~~~~ \\\\ (0 ,  +\\infty)  \u4e0a\u5355\u8c03\u9012\u589e, \u6240\u4ee5  g(x)>g(0)=0, \u6240\u4ee5  f^{\\prime}(x)>  0 , \u6240\u4ee5  f(x)  \u5728  (0,+\\infty)  \u4e0a\u5355\u8c03~~~~\\\\\u9012\u589e, \u7531\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u77e5\n\ng(0)=\\frac{{(e^x+\\sin x -1)}'}{{x}'}|_{x=0}=2.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\u6cd5\u4e8c\u3001\u6570\u5f62\u7ed3\u5408\uff0c\u753b\u5de6\u4fa7\u51fd\u6570f(x)=e^x+sinx\u56fe\u8c61\uff0c\u53f3\u4fa7\u56fe\u8c61g(x)=ax+1~\u8fc7\u5b9a\u70b9.<\/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>\u7ec3\u4e602\uff1a\u5df2\u77e5\u51fd\u6570  f(x)=x\\left(\\mathrm{e}^{x}-1\\right)-a x^{2}(a \\in \\mathbf{R}) .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\(1) \u82e5  f(x)  \u5728  x=-1  \u5904\u6709\u6781\u503c, \u6c42  a  \u7684\u503c;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(2)\u5f53  x&gt;0  \u65f6,  f(x) \\geqslant 0 , \u6c42\u5b9e\u6570  a  \u7684\u53d6\u503c\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 \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7b54\u6848\uff1a(1)  a=\\frac{1}{2} . (2) a \\leqslant 1 \uff1b\u63d0\u793a\uff1a a \\leqslant \\frac{\\mathrm{e}^{x}-1}{x}  \u6052\u6210\u7acb, \u4ee4  h(x)=\\frac{\\mathrm{e}^{x}-1}{x}(x&gt;0), ~~~~~~~~~~~~~~\\\\h(x)  \u5728  (0,+\\infty)  \u4e0a\u5355\u589e,\u7531\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u77e5,  \\lim _{x \\rightarrow 0} h(x)=\\lim _{x \\rightarrow 0} \\frac{(\\mathrm{e}^{x}-1)'}{x'}=\\lim _{x \\rightarrow 0} \\mathrm{e}^{x}=1,  \\therefore a \\leqslant 1 .<\/pre><\/div>\n<\/details>\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\">\u6781\u503c\u70b9\u504f\u79fb<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>5.\u5df2\u77e5\u51fd\u6570f(x)=xe^{-x},\u82e5x_1\\ne x_2,\u4e14f(x_1)=f(x_2),\u6c42\u8bc1\uff1ax_1+x_2&gt;2.~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u63d0\u793a<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u8981\u8bc1x_1+x_2&gt;2,\u53ea\u9700\u8bc1x_2&gt;2-x_1,\u56e0f(x)\u5728(1,+\\infty)\u4e0a\u5355\u51cf\uff0c\u53ea\u9700\u8bc1~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\nf(x_2)&lt;f(2-x_1),\u53c8\u56e0f(x_1)=f(x_2),\u53ea\u9700\u8bc1f(x_1)&lt;f(2-x_1),\u8f6c\u5316\u4e3a~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\u51fd\u6570\u53ea\u9700\u8bc1F(x)=f(x)-f(2-x)&lt;0\u6052\u6210\u7acb.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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-ef41bdf\" data-block-id=\"ef41bdf\"><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-fa998cc\" data-block-id=\"fa998cc\"><style>.stk-fa998cc .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-fa998cc .stk-button:before{box-shadow:0 0 0 2px #7878781a !important}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"\/fabu\/%E6%9E%81%E5%80%BC%E7%82%B9%E5%81%8F%E7%A7%BB-1\/HTML5\/practice.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-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7ec3\u4e60\uff1a\u5df2\u77e5\u51fd\u6570f(x)=x\\ln x\u7684\u56fe\u8c61\u4e0e\u76f4\u7ebfy=m\u4ea4\u4e8e\u4e0d\u540c\u7684\u4e24\u70b9A(x_1,y_1),B(x_2,y_2).~\\\\\n(1)\u6c42m\u7684\u53d6\u503c\u8303\u56f4\uff1b(2)\u6c42\u8bc1\uff1ax_1x_2&lt;\\frac{1}{e^2} .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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 \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(1)(-\\frac{1}{e},0);(2)\u8bf7\u89c2\u770b\u5fae\u8bfe.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\n\n\n\n<div class=\"wp-block-stackable-button-group stk-block-button-group stk-block stk-8b2f3ca\" data-block-id=\"8b2f3ca\"><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-f1077e6\" data-block-id=\"f1077e6\"><style>.stk-f1077e6 .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-f1077e6 .stk-button:before{box-shadow:0 0 0 2px #7878781a !important}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"\/fabu\/%E6%9E%81%E5%80%BC%E7%82%B9%E5%81%8F%E7%A7%BB-2\/HTML5\/practice.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\">\u7aef\u70b9\u6548\u5e94<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>6.\u5df2\u77e5\u51fd\u6570f(x)=a\\ln x+\\frac{1}{2}x^2-\\frac{1}{2}(a\\in R).\u82e5f(x)\\ge0\u5728\u533a\u95f4[1,+\\infty)\u4e0a\u6052\u6210\u7acb\uff0c\u6c42a~~\\\\\u7684\u6700\u5c0f\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 \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a=-1\uff1b\u63d0\u793a\uff1aa\\ge \\frac{-\\frac{1}{2}x^2+\\frac{1}{2}  }{\\ln x} =g(x),{g}'(x)=  \\frac{-x\\ln x+\\frac{x}{2}-\\frac{1}{2x}  }{(\\ln x)^2} ,\u5206\u5b50{h}'(x)\u5355\u51cf\u4e14~~~~~\\\\{h}'(1)=0,\\therefore x&gt;1\u65f6,{h}'(x)&lt;0,\\therefore h(x)\u5355\u51cf\u4e14h(1)=0,\\therefore x&gt;1\u65f6\uff0ch(x)&lt;0\uff0c~~~~~~~~~~~\\\\\\therefore {g}'(x)&lt;0. \\therefore g(x)\u5355\u51cf\uff0c~~~\\therefore g(x)\\ge g(1)=-1.(\u6d1b\u5fc5\u8fbe\u6cd5\u5219)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\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%E7%BB%BC%E5%90%88%E9%A2%98%E2%80%94%E2%80%94%E6%8F%90%E9%AB%98%E7%AF%876\/HTML5\/practice.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-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7ec3\u4e601\uff1a \u5df2\u77e5\u51fd\u6570  f(x)=\\ln x-a(x-1), a \\in \\mathbf{R}, x \\in[1,+\\infty) , \u4e14  f(x) \\leqslant \\frac{\\ln x}{x+1}  \u6052\u6210\u7acb,~~~\\\\\u6c42  a  \u7684\u53d6\u503c\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 \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7b54\u6848\uff1a \\left[\\frac{1}{2},+\\infty\\right) ;\u63d0\u793a:\u89e3  f(x)-\\frac{\\ln x}{x+1}=\\frac{x \\ln x-a\\left(x^{2}-1\\right)}{x+1} , \u4ee4\u5206\u5b50\u90e8\u5206\u4e3a~~~~~~~~~~~~~~~  \\\\g(x)=x \\ln x-a\\left(x^{2}-1\\right)(x \\geqslant 1) , \u5219 g^{\\prime}(x)=\\ln x+1-2 a x , \u4ee4  F(x)=g^{\\prime}(x)=~~~~~~~~~~~~~~\\\\\\ln x+1-2 a x, F^{\\prime}(x)=\\frac{1-2 a x}{x} .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\(1)\u82e5  a \\leqslant 0, g(x) \\geqslant g(1)=0 , \uff0c\u4e0d\u7b26\u5408\u9898\u610f.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\(2)\u82e5  0 &lt; a &lt; \\frac{1}{2}, g(x) \\geqslant g(1)=0 , \u4e0d\u7b26\u5408\u9898\u610f.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\(3)\u82e5  a \\geqslant \\frac{1}{2}, \\therefore g(x)  \u5728  [1,+\\infty)  \u4e0a\u5355\u8c03\u9012\u51cf, \u4ece\u800c  g(x) \\leqslant g(1)=0 .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\u7efc\u4e0a,  a  \u7684\u53d6\u503c\u8303\u56f4\u662f  \\left[\\frac{1}{2},+\\infty\\right) .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n<\/pre><\/div>\n<\/details>\n","protected":false},"excerpt":{"rendered":"<p>\u7aef\u70b9\u6548\u5e94\uff0c\u5206\u79bb\u53c2\u91cf\u3001\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u6c42\u503c<\/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":[25,46],"class_list":["post-1580","post","type-post","status-publish","format-standard","hentry","category-4","tag-25","tag-46"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1580","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=1580"}],"version-history":[{"count":0,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1580\/revisions"}],"wp:attachment":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1580"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1580"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1580"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}