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Popular >

extreme f(x)=(x^2)/(x^2-1)

Solution

extreme points

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

Solution

Maximum (0, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 0

into

\frac{x ^{2}}{x ^{2} - 1} : 0

Maximum (0, 0)

Popular Examples

extreme f(x)=5-2x+3x^2-x^3 extreme points

f (x) = 5 - 2 x + 3 x^{2} - x^{3}

extreme f(x,y)=ln(x^2+y^2-4)extreme points

f (x, y) = ln (x^{2} + y^{2} - 4)

extreme f(x,y)=ln(x+y)extreme points

f (x, y) = ln (x + y)

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

f (x) = - (x + 4)^{3}

extreme f(x,y)=sqrt(4-x^2-4y^2)extreme points

f (x, y) = 4 - x^{2} - 4 y^{2}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x^2)/(x^2-1) ?
The extreme f(x)=(x^2)/(x^2-1) is Maximum(0,0)