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

The critical f(x)= x/(ln(x)) is x=e

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

critical points

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

x = e

Solution steps

\frac{x}{ln ( x )}

Find where

f^{'} (x)

is equal to zero or undefined

x = e, x = 0, x = 1

Identify critical points not in

f (x)

domain

Domain of

\frac{x}{ln ( x )} : 0 < x < 1 or x > 1

\frac{x}{ln ( x )}

is not defined at

x = 0, x = 1

, therefore:

x = e

\frac{z - 3}{z ^{2} - 3 z + 2}

\frac{x ^{2}}{x ^{2} - 9}

f (x) = x (x^{2} - 3)

f (x) = x^{4} - 32 x + 4

f (x) = \frac{x ^{2} + x + 1}{x ^{2}}