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受欢迎的函数 >

extreme y=x^{2/7}(x^2-4)

解答

极值点

y = x^{\frac{2}{7}} (x^{2} - 4)

解答

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

求解步骤

f^{'} (x) = \frac{8 ( 2 ^{\frac{1}{2}} x + 1 ) ( 2 ^{\frac{1}{2}} x - 1 )}{7 x ^{\frac{5}{7}}}

Find intervals:

递减

: - \infty < x < - \frac{1}{2 ^{\frac{1}{2}}},

递增

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

递减

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

递增

: \frac{1}{2 ^{\frac{1}{2}}} < x < \infty

将

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

代入

x^{\frac{2}{7}} (x^{2} - 4) : - \frac{7 ( - \frac{1}{2 ^{\frac{1}{2}}} ) ^{\frac{2}{7}}}{2}

极小值 - \frac{1}{2 ^{\frac{1}{2}}}, - \frac{7 ( - \frac{1}{2 ^{\frac{1}{2}}} ) ^{\frac{2}{7}}}{2}

将

x = 0

代入

x^{\frac{2}{7}} (x^{2} - 4) : 0

极大值 (0, 0)

将

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

代入

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

极小值 (\frac{1}{2 ^{\frac{1}{2}}}, - \frac{7}{2 \cdot 2 ^{\frac{1}{7}}})

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

作图

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