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## Homework Statement

Let ##f\left(\frac{x+y}{2}\right)=\frac{f(x)+f(y)}{2}## for all real x and y. If f'(0) exists and equal -1 and f(0)=1, find f(2).

## Homework Equations

## The Attempt at a Solution

Substituting y=0, 2f(x/2)=f(x)+1. This doesn't seem to be of much help. I don't see how to use the info given about f'(0). I have the equation in two variables x and y, how do I differentiate it?

Any help is appreciated. Thanks!