1. The problem statement, all variables and given/known data Suppose that f(x) is a continuous function on [0,2] with f(0) = f(2). Show that there is a value of x in [0,1] such that f(x) = f(x+1). 2. Relevant equations Intermediate Value Theorem? Extreme Value Theorem? Periodicity? 3. The attempt at a solution For sure there's an f(x1)=f(x2), where x1≠x2, but I don't know how to prove that they're 1 unit apart. Would it also have something to do with the fact that 1 is the half-width of the interval?