1. The problem statement, all variables and given/known data Let f be continuous and differentiable on [a,b], and suppose that f attains its maximum and minimum points c and d, respectively, where c,d belong to [a,b]. Show that f ' (d) = 0 2. Relevant equations 3. The attempt at a solution I thought about using the Mean Value Theorem which states that: f ' (d)=f(b) - f(a) / (b-a) but then didn't know how to continue. Or maybe use Rolle's Theorem, but i couldn't see how that would show that f ' (d) = 0 Any help would be great thanks.