1. The problem statement, all variables and given/known data Let f be continuous in [a,b] and differentiable in (a,b). If f(a)=a and f(b)=b, then prove that f'(x1)+f'(x2)=2 for some x1,x2 ε (a,b) 2. Relevant equations 3. The attempt at a solution Using Lagrange's Mean Value Theorem f'(x)=1 for some x in (a,b). But the question asks the sum of derivatives at 2 points. How do I figure it out?