I need some hints to solve the following:
A function $f(t)$ on an interval $I = (a,b)$ has the mean value property if $f(\frac{s+t}{2}) = \frac{f(s)+f(t)}{2}$ where $s,t\in{I}$. Show that any continuous function on $I$ with the mean value property is affine.
This problem is taken from Chapter 3, Section 4, Question 3 from Theodore Gamelin's Complex Analysis.