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受欢迎的函数 >

extreme f(x)=8x^{1/3}-x^{4/3},-8<= x<= 8

解答

极值点

f (x) = 8 x^{\frac{1}{3}} - x^{\frac{4}{3}}, - 8 \leq x \leq 8

解答

极小值 (- 8, - 32), 极大值 (2, 6 \cdot 2^{\frac{1}{3}}), 极小值 (8, 0)

求解步骤

找到临界点:

x = - 8, x = 0, x = 2, x = 8

8 x^{\frac{1}{3}} - x^{\frac{4}{3}}, - 8 \leq x \leq 8

的定义域

: - 8 \leq x \leq 8

Find intervals:

递增

: - 8 < x < 0,

递增

: 0 < x < 2,

递减

: 2 < x < 8

将极值点

x = - 8

代入

8 x^{\frac{1}{3}} - x^{\frac{4}{3}} \Rightarrow y = - 32

极小值 (- 8, - 32)

将极值点

x = 2

代入

8 x^{\frac{1}{3}} - x^{\frac{4}{3}} \Rightarrow y = 6 2^{\frac{1}{3}}

极大值 (2, 6 \cdot 2^{\frac{1}{3}})

将极值点

x = 8

代入

8 x^{\frac{1}{3}} - x^{\frac{4}{3}} \Rightarrow y = 0

极小值 (8, 0)

极小值 (- 8, - 32), 极大值 (2, 6 \cdot 2^{\frac{1}{3}}), 极小值 (8, 0)

作图

流行的例子

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