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受欢迎的函数 >

extreme x^{1/5}(x^2-4)

解答

极值点

x^{\frac{1}{5}} (x^{2} - 4)

解答

极大值 (- \frac{2}{1 1 ^{\frac{1}{2}}}, \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}}), 极小值 (\frac{2}{1 1 ^{\frac{1}{2}}}, - \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}})

求解步骤

f^{'} (x) = \frac{( 1 1 ^{\frac{1}{2}} x + 2 ) ( 1 1 ^{\frac{1}{2}} x - 2 )}{5 x ^{\frac{4}{5}}}

Find intervals:

递增

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

递减

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

递减

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

递增

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

将

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

代入

x^{\frac{1}{5}} (x^{2} - 4) : \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}}

极大值 (- \frac{2}{1 1 ^{\frac{1}{2}}}, \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}})

将

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

代入

x^{\frac{1}{5}} (x^{2} - 4) : - \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}}

极小值 (\frac{2}{1 1 ^{\frac{1}{2}}}, - \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}})

极大值 (- \frac{2}{1 1 ^{\frac{1}{2}}}, \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}}), 极小值 (\frac{2}{1 1 ^{\frac{1}{2}}}, - \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}})

作图

流行的例子

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e x t re m e f (x) = cos (\frac{4 x}{3})

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