Use analytic methods to find the extreme values of f (x) = (1/x) + lnx on the interval 0.5 ≤ x ≤ 4 and where they occur

F (x) = (1/x) + ln x

At the extreme values, f' (x) = 0

f' (x) = - 1/x^2 + 1/x = 0

(x - 1) / x^2 = 0

x - 1 = 0

x = 1

f (1) = 1/1 + ln 1 = 1

Therefore, the extereme value is 1 and occurs at x = 1.