1. The problem statement, all variables and given/known data A function is continuous/differentiable on the interval [0,3]. I have been given that f(0)=1, f(1)=2, f(3)=2. I need to prove that there exists a c within the interval [0,3] such that f(c) = c. 2. Relevant equations 3. The attempt at a solution f(1)=f(3)=2. From Rolle's theorem, there exists a c within [1,3] such that f`(c)=0. From this I am able to show that at some point c within [1,3] the function must be constant i.e f(c)=k. I am not sure how to show that the constant is equal to the point i.e k=c.