determine local max or local min

a) if b is a positive constant and x>0 , find all critical points of

f(x) = x-blnx.

b) use the second derivative test to determine whether the function has local maximum or local minimum at each critical point.

a= I calculated f'(x), and I obtained f'(x) = 1-b/x , so its critical value would be b.

For b , I believe its derivative is f''(x)= b/x^2 . I know that the second derivative indicates inflection points , concavity , and also local max and min , but I don't how to apply the second derivative test for this particular case! thanks for any help