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Popular Functions >

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

Solution

extreme points

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

Solution

Saddle (0, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Graph

Popular Examples

extreme f(x)=98y^2+x^2-x^2y extreme points

f (x) = 98 y^{2} + x^{2} - x^{2} y

extreme f(x)=((x+4)(x-3)^2)/(x^4(x-1))extreme points

f (x) = \frac{( x + 4 ) ( x - 3 ) ^{2}}{x ^{4} ( x - 1 )}

extreme f(x)=x(6-2x)^2 extreme points

f (x) = x (6 - 2 x)^{2}

extreme f(x)= 1/4 x^4+1/3 x^3-x^2+2/3 extreme points

f (x) = \frac{1}{4} x^{4} + \frac{1}{3} x^{3} - x^{2} + \frac{2}{3}

extreme f(x,y)=-4*(x^2+6x+8)/(y^2+6y+6)extreme points

f (x, y) = - 4 \cdot \frac{x ^{2} + 6 x + 8}{y ^{2} + 6 y + 6}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x^3)/(x^3+1) ?
The extreme f(x)=(x^3)/(x^3+1) is Saddle(0,0)