f(x) = (x-1)lnx
f'(x) = (x-1)/x +lnx
= [x(1+lnx) -1]/x
f'(x) =0
x=1
f''(x) = 1/x^2 + 1/x
f''(1) >0 ( min)
min f(x) = f(1) = 0