What is the extreme g(x)=(x^3)/((x+1)) ?

The extreme g(x)=(x^3)/((x+1)) is Minimum(-3/2 , 27/4),Saddle(0,0)

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extreme g(x)=(x^3)/((x+1))

extreme points

g (x) = \frac{x ^{3}}{( x + 1 )}

Minimum (- \frac{3}{2}, \frac{27}{4}), Saddle (0, 0)

Solution steps

f^{'} (x) = \frac{2 x ^{3} + 3 x ^{2}}{( x + 1 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - \frac{3}{2},

Increasing

: - \frac{3}{2} < x < - 1,

Increasing

: - 1 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{3}{2}

into

\frac{x ^{3}}{x + 1} : \frac{27}{4}

Minimum (- \frac{3}{2}, \frac{27}{4})

Plug

x = 0

into

\frac{x ^{3}}{x + 1} : 0

Saddle (0, 0)

Minimum (- \frac{3}{2}, \frac{27}{4}), Saddle (0, 0)

What is the extreme g(x)=(x^3)/((x+1)) ?
The extreme g(x)=(x^3)/((x+1)) is Minimum(-3/2 , 27/4),Saddle(0,0)