Consider the function f(x) = x - lnx. Find the intervals on which f(x) is increasing and the intervals where it is decreasing. Also determine any relative max or min.

Answer 1

f = x - lnx
f' = 1 - 1/x
f" = 1/x^2

since f" >0 everywhere, f is concave up everywhere

f'=0 when x=1, so that's a local min.