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

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

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

critical points

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

x = - 1

Solution steps

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

Find where

f^{'} (x)

is equal to zero or undefined

x = - 1, x = 1

Identify critical points not in

f (x)

domain

Domain of

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

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

is not defined at

x = 1

, therefore:

x = - 1

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

\frac{x}{x ^{2} - 9}

y = x^{3} + 9 x^{2} + b

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

f (x, y) = - x^{4} - 32 x + y^{3} - 12 y + 7