What is the extreme f(x)=x^3+3x^2+9 ?

The extreme f(x)=x^3+3x^2+9 is Maximum(-2,13),Minimum(0,9)

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extreme f(x)=x^3+3x^2+9

extreme points

f (x) = x^{3} + 3 x^{2} + 9

Maximum (- 2, 13), Minimum (0, 9)

Solution steps

f^{'} (x) = 3 x^{2} + 6 x

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

x^{3} + 3 x^{2} + 9 : 13

Maximum (- 2, 13)

Plug

x = 0

into

x^{3} + 3 x^{2} + 9 : 9

Minimum (0, 9)

Maximum (- 2, 13), Minimum (0, 9)

What is the extreme f(x)=x^3+3x^2+9 ?
The extreme f(x)=x^3+3x^2+9 is Maximum(-2,13),Minimum(0,9)