en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

extreme y=(x^2+9)/(x^2-64)

Solution

extreme points

y = \frac{x ^{2} + 9}{x ^{2} - 64}

Solution

Maximum (0, - \frac{9}{64})

Solution steps

f^{'} (x) = - \frac{146 x}{( x ^{2} - 64 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 8,

Increasing

: - 8 < x < 0,

Decreasing

: 0 < x < 8,

Decreasing

: 8 < x < \infty

Plug

x = 0

into

\frac{x ^{2} + 9}{x ^{2} - 64} : - \frac{9}{64}

Maximum (0, - \frac{9}{64})

Graph

Popular Examples

extreme f(x)=5x+8y extreme points

f (x) = 5 x + 8 y

extreme (cos(x))/(cos(2x))extreme points

\frac{cos ( x )}{cos ( 2 x )}

extreme f(x)=((e^x)/(5+e^x))extreme points

f (x) = (\frac{e ^{x}}{5 + e ^{x}})

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

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

extreme (180ln(x)-300)/(x^2)extreme points

\frac{180 ln ( x ) - 300}{x ^{2}}

Frequently Asked Questions (FAQ)

What is the extreme y=(x^2+9)/(x^2-64) ?
The extreme y=(x^2+9)/(x^2-64) is Maximum(0,-9/64)