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[函数] 求a的最大值

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realnumber posted 2019-8-25 12:00 |Read mode
$f(x)=xe^x-a(x+1)-\ln(x)\ge 0$对任意正实数x恒成立.求a的最大值.
几何画板画了下图是a=1.
推理证明没完成

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kuing posted 2019-8-25 14:06
套路题啊:`xe^x=e^{x+\ln x}\geqslant 1+x+\ln x`

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original poster realnumber posted 2019-8-25 15:14
$xe^x=e^{x+\ln x}\geqslant 1+x+\ln x$复制了下,看下效果


另:a=1还是可以验证的$xe^x=1$时取到等号

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kuing posted 2019-8-25 15:33
回复 3# realnumber

2# 的公式没显示吗?

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original poster realnumber posted 2019-8-25 15:42
回复 4# kuing


    显示的是代码两边两顿号,上标位置的顿号

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kuing posted 2019-8-25 15:45
回复 5# realnumber

难道你们那边网络把 KaTeX 给 Qiang 了?……

PS、那个不是顿号,是左引号(就是台式键盘 Esc 下面那个键,我设了它用于 KaTeX 渲染

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original poster realnumber posted 2019-8-25 16:17
回复 6# kuing


    换了个浏览器,显示正常公式,看来是刚才浏览器不好

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力工 posted 2019-8-25 16:18
这题直接哈做还是挺难的。

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