IMC 2023 Problem 7

Let $V$ be the set of all continuous functions $f\colon [0,1]\to \mathbb{R}$ , differentiable on $(0,1)$ , with the property that $f(0)=0$ and $f(1)=1$ . Determine all $\alpha \in \mathbb{R}$ such that for every $f\in V$ , there exists some $\xi \in (0,1)$ such that $$f(\xi)+\alpha = f'(\xi)$$