en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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})

Popular Examples

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

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

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

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

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

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

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

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

extreme f(x)=3x^4-4x^3-12x^2+5 extreme points

f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 5

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)