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受欢迎的函数 >

extreme x^3-3/2 x^2,-1<= x<= 4

解答

极值点

x^{3} - \frac{3}{2} x^{2}, - 1 \leq x \leq 4

解答

极小值 (- 1, - \frac{5}{2}), 极大值 (0, 0), 极小值 (1, - \frac{1}{2}), 极大值 (4, 40)

求解步骤

找到临界点:

x = - 1, x = 0, x = 1, x = 4

x^{3} - \frac{3}{2} x^{2}, - 1 \leq x \leq 4

的定义域

: - 1 \leq x \leq 4

Find intervals:

递增

: - 1 < x < 0,

递减

: 0 < x < 1,

递增

: 1 < x < 4

将极值点

x = - 1

代入

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

极小值 (- 1, - \frac{5}{2})

将极值点

x = 0

代入

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

极大值 (0, 0)

将极值点

x = 1

代入

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

极小值 (1, - \frac{1}{2})

将极值点

x = 4

代入

x^{3} - \frac{3}{2} x^{2} \Rightarrow y = 40

极大值 (4, 40)

极小值 (- 1, - \frac{5}{2}), 极大值 (0, 0), 极小值 (1, - \frac{1}{2}), 极大值 (4, 40)

作图

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