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受欢迎的函数 >

extreme f(x)=(x-3x^2)^{1/5},-1<= x<= 5

解答

极值点

f (x) = (x - 3 x^{2})^{\frac{1}{5}}, - 1 \leq x \leq 5

解答

极小值 (- 1, - 4^{\frac{1}{5}}), 极大值 (\frac{1}{6}, (\frac{1}{12})^{\frac{1}{5}}), 极小值 (5, - 7 0^{\frac{1}{5}})

求解步骤

找到临界点:

x = - 1, x = 0, x = \frac{1}{6}, x = \frac{1}{3}, x = 5

(x - 3 x^{2})^{\frac{1}{5}}, - 1 \leq x \leq 5

的定义域

: - 1 \leq x \leq 5

Find intervals:

递增

: - 1 < x < 0,

递增

: 0 < x < \frac{1}{6},

递减

: \frac{1}{6} < x < \frac{1}{3},

递减

: \frac{1}{3} < x < 5

将极值点

x = - 1

代入

(x - 3 x^{2})^{\frac{1}{5}} \Rightarrow y = - 4^{\frac{1}{5}}

极小值 (- 1, - 4^{\frac{1}{5}})

将极值点

x = \frac{1}{6}

代入

(x - 3 x^{2})^{\frac{1}{5}} \Rightarrow y = (\frac{1}{12})^{\frac{1}{5}}

极大值 (\frac{1}{6}, (\frac{1}{12})^{\frac{1}{5}})

将极值点

x = 5

代入

(x - 3 x^{2})^{\frac{1}{5}} \Rightarrow y = - 7 0^{\frac{1}{5}}

极小值 (5, - 7 0^{\frac{1}{5}})

极小值 (- 1, - 4^{\frac{1}{5}}), 极大值 (\frac{1}{6}, (\frac{1}{12})^{\frac{1}{5}}), 极小值 (5, - 7 0^{\frac{1}{5}})

作图

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