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受欢迎的函数 >

extreme f(x)=-x^{(3)}+12x^{(2)}+45x-52

解答

极值点

f (x) = - x^{(3)} + 12 x^{(2)} + 45 x - 52

解答

极小值 (4 - 31, 256 - 6231), 极大值 (4 + 31, 256 + 6231)

求解步骤

f^{'} (x) = - 3 x^{2} + 24 x + 45

Find intervals:

递减

: - \infty < x < - 31 + 4,

递增

: - 31 + 4 < x < 31 + 4,

递减

: 31 + 4 < x < \infty

将

x = 4 - 31

代入

- x^{3} + 12 x^{2} + 45 x - 52 : 256 - 6231

极小值 (4 - 31, 256 - 6231)

将

x = 4 + 31

代入

- x^{3} + 12 x^{2} + 45 x - 52 : 256 + 6231

极大值 (4 + 31, 256 + 6231)

极小值 (4 - 31, 256 - 6231), 极大值 (4 + 31, 256 + 6231)

作图

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