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受欢迎的函数 >

extreme f(x)=-6x^3+18x^2+54x-72

解答

极值点

f (x) = - 6 x^{3} + 18 x^{2} + 54 x - 72

解答

极小值 (- 1, - 102), 极大值 (3, 90)

求解步骤

f^{'} (x) = - 18 x^{2} + 36 x + 54

Find intervals:

递减

: - \infty < x < - 1,

递增

: - 1 < x < 3,

递减

: 3 < x < \infty

将

x = - 1

代入

- 6 x^{3} + 18 x^{2} + 54 x - 72 : - 102

极小值 (- 1, - 102)

将

x = 3

代入

- 6 x^{3} + 18 x^{2} + 54 x - 72 : 90

极大值 (3, 90)

极小值 (- 1, - 102), 极大值 (3, 90)

作图

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