let f(x) is continous on [0,1], differentiable on (0,1).

and f(0)=0, f(1)=1.

prove that for any two positive real numbers a and b, there exist two points $\displaystyle 0< x_1< x_2< 1\text{ such that }af'(x_1)+bf'(x_2)=a+b$.

Don't know where to start.