What is the extreme f(x)=-2x^3-24x^2-72x ?

The extreme f(x)=-2x^3-24x^2-72x is Minimum(-6,0),Maximum(-2,64)

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extreme f(x)=-2x^3-24x^2-72x

extreme points

f (x) = - 2 x^{3} - 24 x^{2} - 72 x

Minimum (- 6, 0), Maximum (- 2, 64)

Solution steps

f^{'} (x) = - 6 x^{2} - 48 x - 72

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < - 2,

Decreasing

: - 2 < x < \infty

Plug

x = - 6

into

- 2 x^{3} - 24 x^{2} - 72 x : 0

Minimum (- 6, 0)

Plug

x = - 2

into

- 2 x^{3} - 24 x^{2} - 72 x : 64

Maximum (- 2, 64)

Minimum (- 6, 0), Maximum (- 2, 64)

\frac{1 - x ^{2}}{x}

\frac{5 ( x ^{2} - 1 )}{x ^{2} - 4}

(- 1, - 9), (2, 4)

\frac{8 x}{9 x - 1}

f (x) = tan (4 x)

What is the extreme f(x)=-2x^3-24x^2-72x ?
The extreme f(x)=-2x^3-24x^2-72x is Minimum(-6,0),Maximum(-2,64)