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

The critical (x^2-2x+4)/(x-1) is x=1-sqrt(3),x=1+sqrt(3)

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

critical points

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

x = 1 - 3, x = 1 + 3

Solution steps

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

Find where

f^{'} (x)

is equal to zero or undefined

x = 1 - 3, x = 1 + 3, x = 1

Identify critical points not in

f (x)

domain

Domain of

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

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

is not defined at

x = 1

, therefore:

x = 1 - 3, x = 1 + 3

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

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

f (x) = \frac{1}{3} x - 4

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

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

What is the critical (x^2-2x+4)/(x-1) ?
The critical (x^2-2x+4)/(x-1) is x=1-sqrt(3),x=1+sqrt(3)