(adsbygoogle = window.adsbygoogle || []).push({}); 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(x_{1})=f(x_{2}), where x_{1}≠x_{2}, 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?

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# Homework Help: Continuous Functions, IVT/EVT?

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