Proof Writing · Hard problem

Assume $f$ is differentiable at $a$ and $f$ is not continuous at $a$, and derive a contradiction.

Assume $f$ is not differentiable at $a$ and $f$ is continuous at $a$, and derive a contradiction.

Assume $f$ is continuous at $a$ and show $f$ is differentiable at $a$.

Assume $f$ is not continuous at $a$ and show $f$ is continuous at $a$.