What is the critical f(x)=(x^4-11x^2+4)/((x^2-4)^2) ?

The critical f(x)=(x^4-11x^2+4)/((x^2-4)^2) is x=0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

critical f(x)=(x^4-11x^2+4)/((x^2-4)^2)

critical points

f (x) = \frac{x ^{4} - 11 x ^{2} + 4}{( x ^{2} - 4 ) ^{2}}

x = 0

Solution steps

\frac{x ^{4} - 11 x ^{2} + 4}{( x ^{2} - 4 ) ^{2}}

Find where

f^{'} (x)

is equal to zero or undefined

x = 0, x = - 2, x = 2

Identify critical points not in

f (x)

domain

Domain of

\frac{x ^{4} - 11 x ^{2} + 4}{( x ^{2} - 4 ) ^{2}} : x < - 2 or - 2 < x < 2 or x > 2

\frac{x ^{4} - 11 x ^{2} + 4}{( x ^{2} - 4 ) ^{2}}

is not defined at

x = - 2, x = 2

, therefore:

x = 0

x^{3} - x^{2} - 2 x

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

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

y = e^{x^{2} - 5 x - 1}, - 5 \leq x \leq 5

f (x) = \frac{3 x}{x ^{2} - 1}

What is the critical f(x)=(x^4-11x^2+4)/((x^2-4)^2) ?
The critical f(x)=(x^4-11x^2+4)/((x^2-4)^2) is x=0