What is the critical f(x)=((x^2+1))/((x^2-4)) ?

The critical f(x)=((x^2+1))/((x^2-4)) is x=0

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critical f(x)=((x^2+1))/((x^2-4))

critical points

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

x = 0

Solution steps

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

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 ^{2} + 1}{x ^{2} - 4} : x < - 2 or - 2 < x < 2 or x > 2

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

is not defined at

x = - 2, x = 2

, therefore:

x = 0

f (x) = 6 x^{2} ln (x)

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

y = 3 x^{2} - 2 x + 1

f (x, y) = x^{2} y + y^{3} - 48 y

f (x) = x^{3} + 3 x y^{2} + y^{3} - 15 y - 15 x

What is the critical f(x)=((x^2+1))/((x^2-4)) ?
The critical f(x)=((x^2+1))/((x^2-4)) is x=0