Hi people,

f is a coninuous function on [a,b], and differentiable on ]a, b[ such as: $\displaystyle f(1) \neq f(0)$ and $\displaystyle (\forall x \in ]0;1[): f'(x) \neq 0$

I must show that $\displaystyle (\exists ! \ \alpha \in ]0;1[): 2f(\alpha)-f(0)-f(1)=0$

can you help me please???