1. The problem statement, all variables and given/known data Prove that if f'(x) = g'(x) for all x in an interval (a,b) then f-g is constant on (a,b) then f-g is constant on (a,b) that is f(x) = g(x) + C 2. Relevant equations Let C be a constant Let D be a constant 3. The attempt at a solution f(x) = antiderivative(f'(x)) = f(x) + C g(x)= antiderivative(g'(x)) = g(x) + D f-g = f(x) + C - (g(x) + D) f-g = f(x) - g(x) + C - D but since f'(x) = g'(x) then f(x) = g(x) the only difference is their constant. then, f-g = f(x) - f(x) + C - D f-g = C - D Since C and D are constants then, f-g = constant if C = D then f-g = 0 Note: I feel like I proved it but my notation is wrong since I cannot use f(x) = f(x) + C. I would like guidance for the proper notation to use. The possibility also exists my proof is completely wrong. I would like help Thanks in Advanced!