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

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

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

extreme points

f (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)

f (x) = x^{4} - 8 x^{2}

(x - 1)^{2} + 1

f (x) = \frac{3}{9 - x ^{2}}

f (x) = 2 x + 3

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

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