derivatives calculus

Question

Find the critical numbers, if any, of the given function.

𝑓(𝑥)=2𝑥−ln(𝑥)

answer a comma‑separated list. give the exact form.

Answer 1

f(x) = 2x - lnx f(x) is defined for all x greater than 0.

f'(x) = 2 - 1/x = (2x - 1) / x

f'(x) = 0 when 2x - 1 = 0. So, x = 1/2