$f$ is a real valued function. $f$ is differentiable at a point say $a$.
Does that imply $f$ is continuous in a neighbourhood of $a$?
I think the answer is false, but I can not find a counterexample.
By definition, if a function is differentiable at a point a then the function is defined in a neighbourhood of $a$. Am I right?
We can only conclude that $f$ is continuous at that point $a$.