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受欢迎的函数 >

extreme f(x)=x^3-12x^2+1

解答

极值点

f (x) = x^{3} - 12 x^{2} + 1

解答

极大值 (0, 1), 极小值 (8, - 255)

求解步骤

f^{'} (x) = 3 x^{2} - 24 x

Find intervals:

递增

: - \infty < x < 0,

递减

: 0 < x < 8,

递增

: 8 < x < \infty

将

x = 0

代入

x^{3} - 12 x^{2} + 1 : 1

极大值 (0, 1)

将

x = 8

代入

x^{3} - 12 x^{2} + 1 : - 255

极小值 (8, - 255)

极大值 (0, 1), 极小值 (8, - 255)

作图

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