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

The extreme f(x)=-6x^2-2x^3 is Minimum(-2,-8),Maximum(0,0)

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extreme f(x)=-6x^2-2x^3

extreme points

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

Minimum (- 2, - 8), Maximum (0, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 2

into

- 6 x^{2} - 2 x^{3} : - 8

Minimum (- 2, - 8)

Plug

x = 0

into

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

Maximum (0, 0)

Minimum (- 2, - 8), Maximum (0, 0)

What is the extreme f(x)=-6x^2-2x^3 ?
The extreme f(x)=-6x^2-2x^3 is Minimum(-2,-8),Maximum(0,0)