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Popular >

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)

Popular Examples

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

f (x) = x^{3} + 3 \cdot x^{2} - 9 x + 27

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

f (x) = \frac{x ^{3}}{3} - 4 x^{2} + 7 x + 8

extreme F(x,y)=-x^3+6xy-3y^2+1 extreme points

F (x, y) = - x^{3} + 6 x y - 3 y^{2} + 1

extreme f(xy)=x^3+3y^3+3x^2+3y^2+24 extreme points

f (x y) = x^{3} + 3 y^{3} + 3 x^{2} + 3 y^{2} + 24

extreme f(x,y)=sqrt(-6+2x+6y-x^2-y^2)extreme points

f (x, y) = - 6 + 2 x + 6 y - x^{2} - y^{2}

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)