1. The problem statement, all variables and given/known data Suppose that the function f is continuous on [a,b] and X1 and X2 are in [a,b]. Let K1 and K2 be positive real numbers. Prove that there exist c between X1 and X2 for which f(c) = (K1f(X1) + K2f(X2))/(K1+k2) 2. Relevant equations 3. The attempt at a solution I know I am supposed to have attempted this before asking for help, but honestly I have looked at this problem for over an hour and cannot figure out what to use. I have tried looking at it in terms of Rolles Thrm, Intermediate Value Thrm, and Mean Value Thrm, but nothing is clicking. I also tried manipulating it just by moving things around. I don't seem to be getting anywhere and I'm just hoping someone can point me in the right direction. Then at least I can come up with a decent attempt.