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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

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

Maximum (- 2, 2)

Plug

x = 0

into

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

Minimum (0, - 2)

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

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

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

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

f (x) = x^{4} - 12 x^{3} - 29

f (x) = x e^{\frac{x}{2}}

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