Question

What are the local extrema of `f(x)= lnx/e^x`?

Answer 1

`x=1.763`

Explanation:

Take the derivative of `lnx/e^x` using quotient rule:

`f'(x)=((1/x)e^x-ln(x)(e^x))/e^(2x)`

Take out a `e^x` from the top and move it down to the denominator:

`f'(x)=((1/x)-ln(x))/e^x`

Find when `f'(x)=0` This only happens when the numerator is `0`:

`0=(1/x-ln(x))`

You're going to need a graphing calculator for this one.

`x=1.763`

Plugging in a number under `1.763` would give you a positive outcome while plugging a number above `1.763` would give you a negative outcome. So this is a local maximum.