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受欢迎的函数 >

extreme f(x)=x(1-x)^{2/5}

解答

极值点

f (x) = x (1 - x)^{\frac{2}{5}}

解答

极大值 (\frac{5}{7}, \frac{5 \cdot 2 ^{\frac{2}{5}}}{7 \cdot 7 ^{\frac{2}{5}}}), 极小值 (1, 0)

求解步骤

f^{'} (x) = \frac{- 7 x + 5}{5 ( 1 - x ) ^{\frac{3}{5}}}

Find intervals:

递增

: - \infty < x < \frac{5}{7},

递减

: \frac{5}{7} < x < 1,

递增

: 1 < x < \infty

将

x = \frac{5}{7}

代入

x (1 - x)^{\frac{2}{5}} : \frac{5 \cdot 2 ^{\frac{2}{5}}}{7 \cdot 7 ^{\frac{2}{5}}}

极大值 (\frac{5}{7}, \frac{5 \cdot 2 ^{\frac{2}{5}}}{7 \cdot 7 ^{\frac{2}{5}}})

将

x = 1

代入

x (1 - x)^{\frac{2}{5}} : 0

极小值 (1, 0)

极大值 (\frac{5}{7}, \frac{5 \cdot 2 ^{\frac{2}{5}}}{7 \cdot 7 ^{\frac{2}{5}}}), 极小值 (1, 0)

作图

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