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

The extreme f(x)=x(x+2)^3 is Saddle(-2,0),Minimum(-1/2 ,-27/16)

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

extreme points

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

Saddle (- 2, 0), Minimum (- \frac{1}{2}, - \frac{27}{16})

Solution steps

f^{'} (x) = 2 (x + 2)^{2} (2 x + 1)

Find intervals:

Decreasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < - \frac{1}{2},

Increasing

: - \frac{1}{2} < x < \infty

Plug

x = - 2

into

x (x + 2)^{3} : 0

Saddle (- 2, 0)

Plug

x = - \frac{1}{2}

into

x (x + 2)^{3} : - \frac{27}{16}

Minimum (- \frac{1}{2}, - \frac{27}{16})

Saddle (- 2, 0), Minimum (- \frac{1}{2}, - \frac{27}{16})

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}}

f (x) = \frac{x ^{2} + 1}{x ^{2} - 4}

What is the extreme f(x)=x(x+2)^3 ?
The extreme f(x)=x(x+2)^3 is Saddle(-2,0),Minimum(-1/2 ,-27/16)