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

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

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

critical points

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

x = 0

Solution steps

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

Find where

f^{'} (x)

is equal to zero or undefined

x = 0, x = 2

Identify critical points not in

f (x)

domain

Domain of

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

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

is not defined at

x = 2

, therefore:

x = 0

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

f (x) = - x^{4} + 2 x^{3} + 8 x

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

f (x) = 3 x^{4} - 6 x^{2} + 2

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