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Popular Functions >

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

Solution

extreme points

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

Solution

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)

Graph

Popular Examples

extreme f(x)=x^3+3*x^2-9x+27

extreme f(x)=(x^3)/3-4x^2+7x+8

extreme f(x,y)=ln(1+x^2+y^2)

extreme f(x)=x-3x^{2/3}

extreme f(x)=(x^5)/5-8/3 x^3

Frequently Asked Questions (FAQ)

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