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受欢迎的函数 >

extreme f(x)=x^3-12x^2+36x-1

解答

极值点

f (x) = x^{3} - 12 x^{2} + 36 x - 1

解答

极大值 (2, 31), 极小值 (6, - 1)

求解步骤

f^{'} (x) = 3 x^{2} - 24 x + 36

Find intervals:

递增

: - \infty < x < 2,

递减

: 2 < x < 6,

递增

: 6 < x < \infty

将

x = 2

代入

x^{3} - 12 x^{2} + 36 x - 1 : 31

极大值 (2, 31)

将

x = 6

代入

x^{3} - 12 x^{2} + 36 x - 1 : - 1

极小值 (6, - 1)

极大值 (2, 31), 极小值 (6, - 1)

作图

流行的例子

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