Which set of conditions must a function f satisfy on the interval [a,b] so that the Mean Value Theorem is guaranteed to apply?
a) f is continuous on (a,b) and differentiable on [a,b].
b) f is continuous on [a,b] and differentiable on (a,b).
c) f is differentiable on [a,b] (continuity is not required).
d) f is continuous and differentiable on (a,b).