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

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

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critical f(x)= x/(-2-ln(x))

critical points

f (x) = \frac{x}{- 2 - ln ( x )}

x = \frac{1}{e}

Solution steps

\frac{x}{- 2 - ln ( x )}

Find where

f^{'} (x)

is equal to zero or undefined

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

Identify critical points not in

f (x)

domain

Domain of

\frac{x}{- 2 - ln ( x )} : 0 < x < \frac{1}{e ^{2}} or x > \frac{1}{e ^{2}}

\frac{x}{- 2 - ln ( x )}

is not defined at

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

, therefore:

x = \frac{1}{e}

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