Question

How do you find all extrema for `f(x) = 2x + ln x`?

Answer 1

Find all extrema for `f(x) = 2x + ln x`

`f'(x) = 2+1/x = (2x+1)/x`

`f'(x) =0` at `x=-1/2` and is not defined at `x=0`, but neither `-1/2` nor `0` is in the domain of `f`, so there are no critical numbers. Therefore, there are no extrema.

graph{y=2x+lnx [-18, 18.02, -8.99, 9.04]}