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

The extreme f(x)=-3x^3-9x^2 is Minimum(-2,-12),Maximum(0,0)

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

extreme points

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

Minimum (- 2, - 12), Maximum (0, 0)

Solution steps

f^{'} (x) = - 9 x^{2} - 18 x

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 2

into

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

Minimum (- 2, - 12)

Plug

x = 0

into

- 3 x^{3} - 9 x^{2} : 0

Maximum (0, 0)

Minimum (- 2, - 12), Maximum (0, 0)

What is the extreme f(x)=-3x^3-9x^2 ?
The extreme f(x)=-3x^3-9x^2 is Minimum(-2,-12),Maximum(0,0)