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受欢迎的函数 >

extreme f(x)=x^{2/3}(x-7)

解答

极值点

f (x) = x^{\frac{2}{3}} (x - 7)

解答

极大值 (0, 0), 极小值 (\frac{14}{5}, - \frac{21 \cdot 1 4 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

求解步骤

f^{'} (x) = \frac{5 x - 14}{3 x ^{\frac{1}{3}}}

Find intervals:

递增

: - \infty < x < 0,

递减

: 0 < x < \frac{14}{5},

递增

: \frac{14}{5} < x < \infty

将

x = 0

代入

x^{\frac{2}{3}} (x - 7) : 0

极大值 (0, 0)

将

x = \frac{14}{5}

代入

x^{\frac{2}{3}} (x - 7) : - \frac{21 \cdot 1 4 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}}

极小值 (\frac{14}{5}, - \frac{21 \cdot 1 4 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

极大值 (0, 0), 极小值 (\frac{14}{5}, - \frac{21 \cdot 1 4 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

作图

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