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

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

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

critical points

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

x = 2

Solution steps

\frac{e ^{x}}{x - 1}

Find where

f^{'} (x)

is equal to zero or undefined

x = 2, x = 1

Identify critical points not in

f (x)

domain

Domain of

\frac{e ^{x}}{x - 1} : x < 1 or x > 1

\frac{e ^{x}}{x - 1}

is not defined at

x = 1

, therefore:

x = 2

f (x) = \frac{2 x ^{2} - x - 8}{x ^{2} + 9}

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

f (x) = \frac{x ^{2}}{x ^{2} + x - 90}

f (x) = \frac{6}{( x - 9 )}

f (x) = 8 sin (2 x)