What is the critical f(x)= 1/(x-7)-1/x ?

The critical f(x)= 1/(x-7)-1/x is x= 7/2

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critical f(x)= 1/(x-7)-1/x

critical points

f (x) = \frac{1}{x - 7} - \frac{1}{x}

x = \frac{7}{2}

Solution steps

\frac{1}{x - 7} - \frac{1}{x}

Find where

f^{'} (x)

is equal to zero or undefined

x = \frac{7}{2}, x = 0, x = 7

Identify critical points not in

f (x)

domain

Domain of

\frac{1}{x - 7} - \frac{1}{x} : x < 0 or 0 < x < 7 or x > 7

\frac{1}{x - 7} - \frac{1}{x}

is not defined at

x = 0, x = 7

, therefore:

x = \frac{7}{2}

What is the critical f(x)= 1/(x-7)-1/x ?
The critical f(x)= 1/(x-7)-1/x is x= 7/2