I know I can apply the theorem for the polyniomials to know the number of roots. In fact polynomials are continous whatever $[a,b]$ considered and derivable whatever $(a,b)$.
If the function considered is not a polynomial can I apply this? I thought that I have to verify if the function is continous whatever $[a,b]$ in the domain and derivable whatever $(a,b)$ in the domain? It is right?
Hint: actually there are other functions that are differentiable, and the theorem is general and doesn't restrict to polynomials.
Ex.: $e^x+e^{-x}$ satisfies this problem, as there are two points $a, b$ in some interval such that $f(a) = f(b)$, for some $c$, such that $a<c<b$, and as the derivative changes its sign, then Rolle's Theorem will be satisfied.
Antoher Hint: one thing interesting to note is that if the derivative doesn't change the sign, then it means there aren't two equal values for $f(a)$ and $f(b)$, which means, for example, that you can only have a real root, for the $f$ being zero in some interval.