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

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

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

critical points

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

x = 0

Solution steps

\frac{x ^{2}}{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}}{x ^{2} - 4} : x < - 2 or - 2 < x < 2 or x > 2

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

is not defined at

x = - 2, x = 2

, therefore:

x = 0

f (x) = 2 x^{2} - 7 x - 4

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

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

(- 4, - 3), (2, 5)

f (x) = x^{\frac{3}{5}}

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