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

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

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

critical points

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

x = \frac{1}{2}

Solution steps

\frac{1}{x - 1} - \frac{1}{x}

Find where

f^{'} (x)

is equal to zero or undefined

x = \frac{1}{2}, x = 0, x = 1

Identify critical points not in

f (x)

domain

Domain of

\frac{1}{x - 1} - \frac{1}{x} : x < 0 or 0 < x < 1 or x > 1

\frac{1}{x - 1} - \frac{1}{x}

is not defined at

x = 0, x = 1

, therefore:

x = \frac{1}{2}

f (x) = \frac{1}{( x - 6 ) ( x + 1 )}

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

f (x) = 7 x^{5}

f (x) = \frac{3 x + 6}{x + 2}

f (x) = 4 x^{2} + 16 x + 17

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