For Rolle's Theorem (for mean value as well), why is the interval closed for 1 and open for 2 (see below theorem)?

Rolle's Theorem Let f be a function that satisfies the following three hypotheses: 1. f is continuous on the closed interval [a,b]. 2. f is differentiable on the open interval (a,b). 3. f(a)=f(b) Then there is a number c in (a,b) such that f(c)=0