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

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

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

extreme points

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

Minimum (- 3, 27), Saddle (0, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < - 2,

Increasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

\frac{x ^{3}}{x + 2} : 27

Minimum (- 3, 27)

Plug

x = 0

into

\frac{x ^{3}}{x + 2} : 0

Saddle (0, 0)

Minimum (- 3, 27), Saddle (0, 0)

f (x) = \frac{8 x ^{2}}{x ^{4} + 16}

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

\frac{3 x}{x + 7 ( x - 2 )}

f (x) = \frac{3 - x ^{2}}{x ^{2} + 2 x - 15}

f (x) = 2^{x}

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