What is the extreme f(x)=x^3+18x^2+81x ?

The extreme f(x)=x^3+18x^2+81x is Maximum(-9,0),Minimum(-3,-108)

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extreme f(x)=x^3+18x^2+81x

extreme points

f (x) = x^{3} + 18 x^{2} + 81 x

Maximum (- 9, 0), Minimum (- 3, - 108)

Solution steps

f^{'} (x) = 3 x^{2} + 36 x + 81

Find intervals:

Increasing

: - \infty < x < - 9,

Decreasing

: - 9 < x < - 3,

Increasing

: - 3 < x < \infty

Plug

x = - 9

into

x^{3} + 18 x^{2} + 81 x : 0

Maximum (- 9, 0)

Plug

x = - 3

into

x^{3} + 18 x^{2} + 81 x : - 108

Minimum (- 3, - 108)

Maximum (- 9, 0), Minimum (- 3, - 108)

What is the extreme f(x)=x^3+18x^2+81x ?
The extreme f(x)=x^3+18x^2+81x is Maximum(-9,0),Minimum(-3,-108)