How to know if a function has local or absolute extreme?

Using math expression, can i know whether the function has local or absolute extreme by inputting the critical point of function's derivative into original function? Assume f(x)'= 0 at x = 1 and x = 2, and x = 1 is the point where function has maximum and x = 2 is the ponit where function has minimum, so how do know we that at x = 2 it is local or absolute max and x = 1 it is local or absolute min ?