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Popular >

extreme (x^2+1)/(x^2-1)

Solution

extreme points

\frac{x ^{2} + 1}{x ^{2} - 1}

Solution

Maximum (0, - 1)

Solution steps

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

Maximum (0, - 1)

Graph

Popular Examples

extreme f(x)=(x^2-12)/(x-4)extreme points

f (x) = \frac{x ^{2} - 12}{x - 4}

extreme ((x^2)/4-x/2-1/4)^2 extreme points

(\frac{x ^{2}}{4} - \frac{x}{2} - \frac{1}{4})^{2}

extreme f(x,y)=2x^2+3y^2-4x-6 extreme points

f (x, y) = 2 x^{2} + 3 y^{2} - 4 x - 6

extreme f(x,y)=sqrt(400-100x^2-16y^2)extreme points

f (x, y) = 400 - 100 x^{2} - 16 y^{2}

extreme f(x,y)=x^3+y^3+3xy^2-18(x+y)extreme points

f (x, y) = x^{3} + y^{3} + 3 x y^{2} - 18 (x + y)

Frequently Asked Questions (FAQ)

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