设函数[tex=3.714x1.286]ILxTGSNsFVqbb4UrB1q2og==[/tex]具有二阶导数且[tex=4.214x1.286]YRReUQzIsdcIgxj5peM19NRfM/N7sJwKZdaYKnU6eS8=[/tex],直线[tex=1.0x1.286]TNZJ7SbeR9v3+IiQfw5EtQ==[/tex]是曲线[tex=3.714x1.286]ILxTGSNsFVqbb4UrB1q2og==[/tex]上任一点 [tex=3.214x1.286]9ez2b9qo3tkyk3Ytj6uvLQ==[/tex]处的切线[tex=4.214x1.286]gde98ib3mRMZNaNvQL1APPN1/rQTeZB/TWx/fQOJZzM=[/tex].记直线[tex=1.0x1.286]TNZJ7SbeR9v3+IiQfw5EtQ==[/tex]与曲线[tex=3.714x1.286]ILxTGSNsFVqbb4UrB1q2og==[/tex]以及直线[tex=2.357x1.286]F20DA9b5PZyvxJH27l4LOQ==[/tex],[tex=2.357x1.286]jgIRiGqlkdCMqO92sJAASg==[/tex]所围成的图形的面积为[tex=1.786x1.286]9PL6s5d10njRp1ZVGReFNQ==[/tex].证明:[tex=1.786x1.286]9PL6s5d10njRp1ZVGReFNQ==[/tex]的最小值[tex=5.286x1.714]SACYgy6I9Uodm/6ZmfQc6eW7CapSQ4N/rXDqzR2affdNZVAg/1cmOOL/POrOx5Ua[/tex][tex=3.786x2.357]MR8iE8IK/XVXB+o5sM8zas4MuUdCY43q62vfbdDAxcc=[/tex][tex=4.571x2.429]KEskdFvxflbt/GW6hsSi7QbV8h0e0k/1UZEEWEOI2Mw=[/tex].

2022-06-29

设函数[tex=3.714x1.286]ILxTGSNsFVqbb4UrB1q2og==[/tex]具有二阶导数且[tex=4.214x1.286]YRReUQzIsdcIgxj5peM19NRfM/N7sJwKZdaYKnU6eS8=[/tex],直线[tex=1.0x1.286]TNZJ7SbeR9v3+IiQfw5EtQ==[/tex]是曲线[tex=3.714x1.286]ILxTGSNsFVqbb4UrB1q2og==[/tex]上任一点 [tex=3.214x1.286]9ez2b9qo3tkyk3Ytj6uvLQ==[/tex]处的切线[tex=4.214x1.286]gde98ib3mRMZNaNvQL1APPN1/rQTeZB/TWx/fQOJZzM=[/tex].记直线[tex=1.0x1.286]TNZJ7SbeR9v3+IiQfw5EtQ==[/tex]与曲线[tex=3.714x1.286]ILxTGSNsFVqbb4UrB1q2og==[/tex]以及直线[tex=2.357x1.286]F20DA9b5PZyvxJH27l4LOQ==[/tex],[tex=2.357x1.286]jgIRiGqlkdCMqO92sJAASg==[/tex]所围成的图形的面积为[tex=1.786x1.286]9PL6s5d10njRp1ZVGReFNQ==[/tex].证明:[tex=1.786x1.286]9PL6s5d10njRp1ZVGReFNQ==[/tex]的最小值[tex=5.286x1.714]SACYgy6I9Uodm/6ZmfQc6eW7CapSQ4N/rXDqzR2affdNZVAg/1cmOOL/POrOx5Ua[/tex][tex=3.786x2.357]MR8iE8IK/XVXB+o5sM8zas4MuUdCY43q62vfbdDAxcc=[/tex][tex=4.571x2.429]KEskdFvxflbt/GW6hsSi7QbV8h0e0k/1UZEEWEOI2Mw=[/tex].

答案：

解:切线方程为[tex=4.429x1.286]9KMKTOYd2vv6Li5EuuMI1g==[/tex][tex=4.786x1.286]P/fLMWq+IkCYosDnQtWztz6wy6lFeoUX/GtfeXGy8Ro=[/tex],因此所求面积为[tex=17.286x6.071]a0s3MH7cLIdmiBRR0YN060P04s5EBWQmQGBxp3huG5EMDZP1fSIyy59F10GRJXMdMGwC0vCawArOBz9VPWtvhUAFiiAvYa8F56GnPHr2g6sVHng779Y4RZ+Uv1NYIgY5zFuCTRuHwA6sniwXOGuuC4l7FH0XkttwUkGsfmc2vYrHfdPlri7JgfpGQzKXm3b/tEPysGMdP3WjHEaHzWhA9Hto9Y7aswV+VH7R1pnev24=[/tex][tex=3.643x2.071]9ZS6E9SWwTgWcz4JbqzryNlzX2JKBV7qvL7obm8ylaE=[/tex][tex=6.0x2.357]/Ct4zgqkDjOrCNyHxpQhxfSRvBT409648lEfO6UmtpisgFK6MXEB6qPXYJwk9f+UWAnc37al7TJMKVhxOv0nDw==[/tex].令[tex=4.357x2.071]HtMTlQ0EAI9UKEE0B052AbU6DZ+2qQDsUFQI7U6KOjM=[/tex]得惟一驻点[tex=2.286x2.0]zYlJRS/CxwRTI2aHUYzaGLuw33SD/3IT9GogiMgI4sU=[/tex],易知该驻点为极小值点,从而必为[tex=1.786x1.286]9PL6s5d10njRp1ZVGReFNQ==[/tex]取得最小值的点,因此[tex=5.286x1.714]SACYgy6I9Uodm/6ZmfQc6eTOwy8eOFc1+XIH6zdnhnAa0xTsFE7rAE/WXlut+VlR[/tex][tex=4.071x2.357]FD+lqy31YdffBwVZnouaPYY564GwZmgN9nndIwJrKmLDiJuVEpKqHHMvQ60w2H39[/tex][tex=3.786x2.357]MR8iE8IK/XVXB+o5sM8zas4MuUdCY43q62vfbdDAxcc=[/tex][tex=4.571x2.429]KEskdFvxflbt/GW6hsSi7QbV8h0e0k/1UZEEWEOI2Mw=[/tex].

举一反三

内容

0
判断下列命题是否为真：（1）[tex=3.643x1.357]/5abqJjwKZ1qr+6hsVFF5EBvfq3ggOFNlHMClz0h9nk=[/tex]（2）[tex=2.929x1.357]rGJpyjIjJpbcoBTWxP0Jiw==[/tex]（3）[tex=4.5x1.357]2wycHMoqU83MyEp17iBils58bR7YLuCTI2G9NVAdlfY=[/tex]（4）[tex=5.214x1.357]CTz2gu+IIm1GgNmYMGaduCRtA41wnW4WqwRWwEhq6aA=[/tex]（5）[tex=4.857x1.357]1DcE2BMMOaZhTuxR/mjgsboXxfg5ET59Dp4I/jjEDuw=[/tex]（6）[tex=4.643x1.357]BSryrsQYOvTP2hTWRu6t4nAuJwlSs4L9jaq70EpB+Us=[/tex]（7）若[tex=6.0x1.357]y0IZLUnBO88nR8WBZYvd7QXv5S1OMINV5cQNzPyiyAc=[/tex]，则[tex=3.429x1.357]1brfPwTkVVIX4GfoMIUskA==[/tex]（8）若[tex=7.643x1.357]MhLfJXZnhbXiB0x3oNtFzThV4Y1mJxe1VYr7PkJE/T6hmTD3WWp+UxbNwvUQ6DHk[/tex]，则[tex=4.143x1.357]LZUA94ISo1po5HWsOVeBCjo0rMvj7uw3bGw5HiZenrI=[/tex]
1
某人对商品x的需求函数是[tex=5.214x1.214]0m6eBd5eyK0NjuxeKfwtIw==[/tex]，[tex=4.214x1.214]I717YsPbj8Rnym1v2XQ+sFNkUl7mqUsGwbjwjXmy2xc=[/tex]，这里[tex=0.571x1.0]Za328cIB4SeR7rrzY+MM5Q==[/tex]是[tex=0.571x0.786]ZSLOI4fiO1oAbVC5M8IVkA==[/tex]的价格。如果商品x 的价格是0.5元，那么他对商品x的需求价格弹性是未知类型：{'options': ['-10', '- 1/5', '-1/10', '\xa0- 1/3'], 'type': 102}
2
>>>x= [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9]>>>print(x.sort()) 语句运行结果正确的是( )。 A: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] B: [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9] C: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0] D: ['2', '4', '0', '6', '10', '7', '8', '3', '9', '1', '5']
3
以下生产函数,哪些呈现递增、递减或不变的规模报酬? (1) [tex=7.357x1.357]XSZKoB4IYW0Gbq0fT0VGdpSNRrjnZD2xnWmU/f2IQp4=[/tex];(2) [tex=6.143x1.429]okrkibdGbRVHrBdqyMxExPok6BrwJhbIMhhTVHL2hFY=[/tex] ;(3) [tex=5.643x1.429]WNb39kBjYbA4R0b5xpycO6BfDidhMTx+CJojlGf/sDI=[/tex] ;(4) [tex=5.714x1.429]Q1cnNTo244ZQVvSfsdGe76qdAT4+f111LLhIL1D55FU=[/tex] ;(5) [tex=6.071x1.5]dAAyESpT8Py6v5ArhYZSS1Xe6blQtgeWYyWAhAqHmXM=[/tex];(6) [tex=7.857x1.357]anw59zoD7yqd/X4i/8QKFNeAPD+1K7uzfET7zeE1EfA=[/tex](7) [tex=12.357x1.786]+PkwdonbCCj8Z9ceWnLUNRl3BL2oikAY4KmA/JNGWpzhYYTWMLiiFXC1n+tRPPVU4A8W2gY6kNpJrJFuuPY6SA==[/tex]
4
求下列函数的单调区间、凹凸区间、极值点、拐点和渐近线,并绘图(图略).(1) [tex=6.643x1.5]bfylM61K4fB2dxr0OSsfGnNoGCHA31PVTv+V6O1K8rw=[/tex](2)[tex=7.643x1.571]v8BogKFXW30N+HMJ7QR6DhxEDs5D0riUpoj095rhlGc=[/tex](3) [tex=3.714x2.143]X1YpNX45Pb+t3RD9Lv2Xa/npVx6iPUE04M2Y4K2k/cw=[/tex](4) [tex=5.071x3.0]4TWEbfJ+QFPbBo6PXWTsCrjc66tVrHBOTlDUBxhSpARz8/MfCO/nUo/gE3SyIffw[/tex](5)[tex=6.571x2.429]gt+k1kCw/+VFBVaKddmG6PvDvxiTdyZFXDwIPBeuGlw=[/tex](6)[tex=5.643x1.429]Hzyd6Qvm69qjRqgBIuKTx/cTmFyy56Dt2K/GC7NoCdc=[/tex](7) [tex=7.143x1.214]CwtdUElTamN1NqF0aKHeWGdaXEazoOnz3w3c67izzuE=[/tex](8)[tex=4.714x2.786]cxjZEag+Wbr67lAUIC3Slk2OV17yHgezOhFRferr5F0=[/tex].