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

The critical f(x)=(ln(x))/(sqrt(x)) is x=e^2

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critical f(x)=(ln(x))/(sqrt(x))

critical points

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

x = e^{2}

Solution steps

\frac{ln ( x )}{x}

Find where

f^{'} (x)

is equal to zero or undefined

x = e^{2}, x = 0

Identify critical points not in

f (x)

domain

Domain of

\frac{ln ( x )}{x} : x > 0

\frac{ln ( x )}{x}

is not defined at

x = 0

, therefore:

x = e^{2}

What is the critical f(x)=(ln(x))/(sqrt(x)) ?
The critical f(x)=(ln(x))/(sqrt(x)) is x=e^2