Which set of hypotheses on a real-valued function f defined on [a,b] is sufficient to guarantee that some number c in (a,b) satisfies f′(c)=0?
a) f is continuous on (a,b), differentiable on (a,b), and f(a)=f(b).
b) f is continuous on [a,b], differentiable on (a,b), and f(a)=f(b).
c) f is continuous on [a,b], differentiable on (a,b), with no restriction on f(a) and f(b).
d) f is continuous on [a,b], differentiable on (a,b), and f(a)<f(b).