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[函数] 如何不求导求最值

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math505 posted 2023-2-25 21:21 from mobile |Read mode
$f(x)=\frac{x^3-x}{x^2+1},-1<x<1$,
不求导的方法求$f(x)$的最值.

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hbghlyj posted 2023-2-25 21:35
补充)

结果是$f(x)\in\left[-\sqrt{\frac{5 \sqrt{5}}{2}-\frac{11}{2}},\sqrt{\frac{5 \sqrt{5}}{2}-\frac{11}{2}}\right]$
最值点$x=\pm\sqrt{\sqrt{5}-2}$

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