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受欢迎的函数 >

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

解答

极值点

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

解答

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

求解步骤

找到临界点:

x = - 1, x = 0, x = \frac{2}{5}, x = 1

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

的定义域

: - 1 \leq x \leq 1

Find intervals:

递减

: - 1 < x < 0,

递增

: 0 < x < \frac{2}{5},

递减

: \frac{2}{5} < x < 1

将极值点

x = - 1

代入

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

极大值 (- 1, 2)

将极值点

x = 0

代入

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

极小值 (0, 0)

将极值点

x = \frac{2}{5}

代入

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

极大值 (\frac{2}{5}, \frac{3 \cdot 2 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

将极值点

x = 1

代入

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

极小值 (1, 0)

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

作图

流行的例子

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