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

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

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

extreme points

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

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

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

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

Minimum (- 2, - 2)

Plug

x = 0

into

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

Maximum (0, 2)

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

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

f (x) = 121 - x^{2}

f (x) = \frac{x ^{3}}{x ^{2} - 4}

\frac{2 x + 3}{x - 1}

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

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