If f(x) is differentiable at x=a , then consider the following...

If a function $f(x)$ is differentiable at a point $x=a$, then it is necessarily continuous at that point. This makes Statement I correct.

By the definition of continuity at a point $x=a$, the limit of the function as $x$ approaches $a$ must be equal to the value of the function at $a$. Thus, $\lim\limits_{x\to a}f(x)=f(a)$. This makes Statement II correct.

Therefore, both statements I and II are correct.

Answer: Both I and II