The contrapositive of the statement 'If a function $f$ is differentiable at $x=a$, then $f$ is continuous at $x=a$' is:

1. A.If $f$ is not differentiable at $x=a$, then $f$ is not continuous at $x=a$.
2. B.If $f$ is continuous at $x=a$, then $f$ is differentiable at $x=a$.
3. C.If $f$ is not continuous at $x=a$, then $f$ is not differentiable at $x=a$.
4. D.If $f$ is continuous at $x=a$, then $f$ is not differentiable at $x=a$.