Assume $f$ is a function such that $f(a)=f(b)=0$.
The function is defined and continuous on the domain $[a,b]$ and is differentiable on $(a,b)$.
Prove that there is a point $c$ in that domain such that $f(c)=f'(c)$.
I don't know how to solve this problem, I wanted to approach this by assuming that there is a number of possible continuous functions that belong to the domain and at least one of them has a derivative that's equal to the output at point $c$. Other than that, I'm clueless, please help me out!