What is the extreme f(x)=x^3+6x^2+9x ?

The extreme f(x)=x^3+6x^2+9x is Maximum(-3,0),Minimum(-1,-4)

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extreme f(x)=x^3+6x^2+9x

extreme points

f (x) = x^{3} + 6 x^{2} + 9 x

Maximum (- 3, 0), Minimum (- 1, - 4)

Solution steps

f^{'} (x) = 3 x^{2} + 12 x + 9

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < - 1,

Increasing

: - 1 < x < \infty

Plug

x = - 3

into

x^{3} + 6 x^{2} + 9 x : 0

Maximum (- 3, 0)

Plug

x = - 1

into

x^{3} + 6 x^{2} + 9 x : - 4

Minimum (- 1, - 4)

Maximum (- 3, 0), Minimum (- 1, - 4)

f (x) = (x - 3)^{3} + 4

f (x) = 7 - 2 x - 3 x^{2}

f (x) = x^{3} - 6 x^{2} + 9 x + 3

f (x) = \frac{3}{4} x - 6

f (x) = - 3 x^{2} - 12 x + 15

What is the extreme f(x)=x^3+6x^2+9x ?
The extreme f(x)=x^3+6x^2+9x is Maximum(-3,0),Minimum(-1,-4)