What is the extreme f(x)=2x^3+9x^2+12x ?

The extreme f(x)=2x^3+9x^2+12x is Maximum(-2,-4),Minimum(-1,-5)

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extreme f(x)=2x^3+9x^2+12x

extreme points

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

Maximum (- 2, - 4), Minimum (- 1, - 5)

Solution steps

f^{'} (x) = 6 x^{2} + 18 x + 12

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < - 1,

Increasing

: - 1 < x < \infty

Plug

x = - 2

into

2 x^{3} + 9 x^{2} + 12 x : - 4

Maximum (- 2, - 4)

Plug

x = - 1

into

2 x^{3} + 9 x^{2} + 12 x : - 5

Minimum (- 1, - 5)

Maximum (- 2, - 4), Minimum (- 1, - 5)

What is the extreme f(x)=2x^3+9x^2+12x ?
The extreme f(x)=2x^3+9x^2+12x is Maximum(-2,-4),Minimum(-1,-5)