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受欢迎的函数 >

extreme f(x)=x(ln(x))^2

解答

极值点

f (x) = x (ln (x))^{2}

解答

极大值 (\frac{1}{e ^{2}}, \frac{4}{e ^{2}}), 极小值 (1, 0)

求解步骤

f^{'} (x) = ln^{2} (x) + 2 ln (x)

Find intervals:

递增

: 0 < x < \frac{1}{e ^{2}},

递减

: \frac{1}{e ^{2}} < x < 1,

递增

: 1 < x < \infty

将

x = \frac{1}{e ^{2}}

代入

x ln^{2} (x) : \frac{4}{e ^{2}}

极大值 (\frac{1}{e ^{2}}, \frac{4}{e ^{2}})

将

x = 1

代入

x ln^{2} (x) : 0

极小值 (1, 0)

极大值 (\frac{1}{e ^{2}}, \frac{4}{e ^{2}}), 极小值 (1, 0)

作图

流行的例子

extreme f(x)=(x/(\sqrt[3]{x^2-1)})

e x t re m e f (x) = (\frac{x}{3 x ^{2} - 1})

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