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

The extreme f(x)=-x^3-12x^2 is Minimum(-8,-256),Maximum(0,0)

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extreme f(x)=-x^3-12x^2

extreme points

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

Minimum (- 8, - 256), Maximum (0, 0)

Solution steps

f^{'} (x) = - 3 x^{2} - 24 x

Find intervals:

Decreasing

: - \infty < x < - 8,

Increasing

: - 8 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 8

into

- x^{3} - 12 x^{2} : - 256

Minimum (- 8, - 256)

Plug

x = 0

into

- x^{3} - 12 x^{2} : 0

Maximum (0, 0)

Minimum (- 8, - 256), Maximum (0, 0)

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

f (x) = 90 x^{2} - 0.2 x^{4}

f (x \cdot y) = 3 x^{2} - 4 x y + 3 y^{2} + 8 x - 17 y + 5

x^{3} - 16 x y + 4 y^{2} + 16 x^{2} - 12 x + 5

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

What is the extreme f(x)=-x^3-12x^2 ?
The extreme f(x)=-x^3-12x^2 is Minimum(-8,-256),Maximum(0,0)