If f is continuous at a, must f be differentiable at a?

Choose the correct answer below.
A. No. If f is continuous at a, it is not necessarily true that the limit that defines f' exists at a.

B. No. If f is differentiable at a, then f is not continuous at a. The contrapositive of this statement therefore states, if f is continuous at
a, then f is not differentiable at a.

C. Yes. If f is continuous at a, it is necessarily true that the limit that defines f' exists at a.

D. Yes. If f is differentiable at a, then f is continuous at a. The contrapositive of this statement therefore states, if f is continuous at a, then f is differentiable at a.