I was solving past exams of calculus course and I've encounter with a problem, which I couldn't figure out how to solve.The question is following;
Prove that whether the given statement is true or false:
Suppose that $f(x)$ is continuous on $[0, 2]$ and $f(0)=f(2)$. Then there exists a number $c\in [0, 1]$ such that $f(c) = f(c + 1)$.
By just reading the question, you want to say "use Mean Value Theorem or Rolle's theorem" but we don't know whether $f(x)$ is differentiable on the interval, at least it is now given, so I am totally stuck.I would appreciate any help.