en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

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

Solution

extreme points

\frac{x ^{2} + 1}{x ^{2} - 4}

Solution

Maximum (0, - \frac{1}{4})

Solution steps

f^{'} (x) = - \frac{10 x}{( x ^{2} - 4 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

\frac{x ^{2} + 1}{x ^{2} - 4} : - \frac{1}{4}

Maximum (0, - \frac{1}{4})

Graph

Popular Examples

extreme f(x,y)=-x^2-y^2+8x+6y

extreme f(x)=x+e^{-2x}

extreme f(x)=-x(x+2)(x-2)

extreme f(x)=6x^5-10x^3

extreme f(x,y)=-x^2-y^2

Frequently Asked Questions (FAQ)

What is the extreme (x^2+1)/(x^2-4) ?
The extreme (x^2+1)/(x^2-4) is Maximum(0,-1/4)