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受欢迎的函数 >

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

解答

极值点

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

解答

极大值 (0, - 12), 极小值 (4, - \frac{44}{3})

求解步骤

f^{'} (x) = \frac{x ^{2}}{4} - x

Find intervals:

递增

: - \infty < x < 0,

递减

: 0 < x < 4,

递增

: 4 < x < \infty

将

x = 0

代入

\frac{1}{12} x^{3} - \frac{1}{2} x^{2} - 12 : - 12

极大值 (0, - 12)

将

x = 4

代入

\frac{1}{12} x^{3} - \frac{1}{2} x^{2} - 12 : - \frac{44}{3}

极小值 (4, - \frac{44}{3})

极大值 (0, - 12), 极小值 (4, - \frac{44}{3})

作图

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