What is the extreme f(x)=-1/3 x^3-x^2-12 ?

The extreme f(x)=-1/3 x^3-x^2-12 is Minimum(-2,-40/3),Maximum(0,-12)

extreme f(x)=-1/3 x^3-x^2-12

extreme points

f (x) = - \frac{1}{3} x^{3} - x^{2} - 12

Minimum (- 2, - \frac{40}{3}), Maximum (0, - 12)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 2

into

- \frac{1}{3} x^{3} - x^{2} - 12 : - \frac{40}{3}

Minimum (- 2, - \frac{40}{3})

Plug

x = 0

into

- \frac{1}{3} x^{3} - x^{2} - 12 : - 12

Maximum (0, - 12)

Minimum (- 2, - \frac{40}{3}), Maximum (0, - 12)

f (x) = - \frac{24 x}{x ^{2} + 9}

- 2 x^{2} - 12 x - 17

f (x) = 5 x e^{- x}, 0 \leq x \leq 2

f (x) = 2 x^{3} - 9 x^{2} + 60 x + 8

f (x) = 150 x - 2 x^{3}

What is the extreme f(x)=-1/3 x^3-x^2-12 ?
The extreme f(x)=-1/3 x^3-x^2-12 is Minimum(-2,-40/3),Maximum(0,-12)