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受欢迎的函数 >

extreme f(x)=(x^3)/3-5x^2+16x-100

解答

极值点

f (x) = \frac{x ^{3}}{3} - 5 x^{2} + 16 x - 100

解答

极大值 (2, - \frac{256}{3}), 极小值 (8, - \frac{364}{3})

求解步骤

f^{'} (x) = x^{2} - 10 x + 16

Find intervals:

递增

: - \infty < x < 2,

递减

: 2 < x < 8,

递增

: 8 < x < \infty

将

x = 2

代入

\frac{x ^{3}}{3} - 5 x^{2} + 16 x - 100 : - \frac{256}{3}

极大值 (2, - \frac{256}{3})

将

x = 8

代入

\frac{x ^{3}}{3} - 5 x^{2} + 16 x - 100 : - \frac{364}{3}

极小值 (8, - \frac{364}{3})

极大值 (2, - \frac{256}{3}), 极小值 (8, - \frac{364}{3})

作图

流行的例子

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