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

Find all extrema for $f \left(x\right) = 2 x + \ln x$
$f ' \left(x\right) = 2 + \frac{1}{x} = \frac{2 x + 1}{x}$
$f ' \left(x\right) = 0$ at $x = - \frac{1}{2}$ and is not defined at $x = 0$, but neither $- \frac{1}{2}$ nor $0$ is in the domain of $f$, so there are no critical numbers. Therefore, there are no extrema.