1. The problem statement, all variables and given/known data Let f and g be two continuous functions that are defined on [a,b] and differentiable on (a,b). Claim: If f'=g' on (a,b), then there exists a constant k such that f(x)=g(x)+k for all x in [a,b] 2. Relevant equations 3. The attempt at a solution Let h:[a,b]->R be defined by h(x)=g(x)+k-f(x) h is continuous and differentiable on [a,b] by the assumptions of f and g already made. Since f'=g' => g'-f'=0 So h'(x) = g'(x) - f'(x) = 0 By the mean value theorem, there exists a c in (a,b) so that 0=(h(b)-h(a))/(b-a) => h(a)=h(b) I think I showed rolle's theorem. I am trying to use my assumption that f'=g' to show the claim. Any hints on this?