For the function, find all critical points or determine that no such points exist.

Answer

We find the derivative using the quotient rule.

The derivative *f*'(*x*) is undefined when *x* ≤ 0, but since we're only looking at the function *f* for *x* > 0, we don't find any critical points because *f*'(*x*) is undefined. To find where *f*'(*x*) = 0, we find where the numerator is equal to 0.

If

*ln* *x* - 1 = 0

then

*ln* *x* = 1,

therefore

*x* = *e*.

This is our only critical point. This makes sense on the graph, if we zoom in a lot: