What is the extreme f(x)=-x^3-3x^2-1 ?

The extreme f(x)=-x^3-3x^2-1 is Minimum(-2,-5),Maximum(0,-1)

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extreme f(x)=-x^3-3x^2-1

extreme points

f (x) = - x^{3} - 3 x^{2} - 1

Minimum (- 2, - 5), Maximum (0, - 1)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 2

into

- x^{3} - 3 x^{2} - 1 : - 5

Minimum (- 2, - 5)

Plug

x = 0

into

- x^{3} - 3 x^{2} - 1 : - 1

Maximum (0, - 1)

Minimum (- 2, - 5), Maximum (0, - 1)

What is the extreme f(x)=-x^3-3x^2-1 ?
The extreme f(x)=-x^3-3x^2-1 is Minimum(-2,-5),Maximum(0,-1)