- #1

- 7

- 0

## Homework Statement

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).

## Homework Equations

Intermediate Value Theorem?

Extreme Value Theorem?

Periodicity?

## 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?