Question

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

Answer 1

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.