What is the extreme f(x)=7-6x^2-x^3 ?

The extreme f(x)=7-6x^2-x^3 is Minimum(-4,-25),Maximum(0,7)

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extreme f(x)=7-6x^2-x^3

extreme points

f (x) = 7 - 6 x^{2} - x^{3}

Minimum (- 4, - 25), Maximum (0, 7)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 4

into

7 - 6 x^{2} - x^{3} : - 25

Minimum (- 4, - 25)

Plug

x = 0

into

7 - 6 x^{2} - x^{3} : 7

Maximum (0, 7)

Minimum (- 4, - 25), Maximum (0, 7)

What is the extreme f(x)=7-6x^2-x^3 ?
The extreme f(x)=7-6x^2-x^3 is Minimum(-4,-25),Maximum(0,7)