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[函数] 2021年全国卷甲第21题 导数幂与指数函数的商

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isee posted 2021-6-9 22:02 |Read mode
Last edited by isee 2021-7-21 21:28$y=a^x$的导数正式登场了……

分参后就化为$y=\frac{\ln x}{x}$这个常见函数的性质了


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题:
21. 已知\(a>0\)且$a\ne 1$,函数\(f(x)=\frac{x^a}{a^x}(x>0)\).
(1)当$a=2$时,求$f\left( x \right)$的单调区间;
(2)若曲线\(y=f\left( x \right)\)与直线\(y=1\)有且仅有两个交点,求`a`的取值范围.
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