What is the critical (x^2)/((x^2-1)) ?

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

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critical (x^2)/((x^2-1))

critical points

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

x = 0

Solution steps

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

Find where

f^{'} (x)

is equal to zero or undefined

x = 0, x = - 1, x = 1

Identify critical points not in

f (x)

domain

Domain of

\frac{x ^{2}}{x ^{2} - 1} : x < - 1 or - 1 < x < 1 or x > 1

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

is not defined at

x = - 1, x = 1

, therefore:

x = 0

f (x, y) = 4 x^{4} + 4 y^{4} - x y

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

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

f (y) = x^{2} + 6 x + 9

2 x^{3} - 3 x^{2} - 12 x + 15