All the definitions i know refers to situation where I can tell if funcion f is continuous or diferentiable in particular point a. But now i got an assignment, where i must tell if function is continuous and diferentible in general?

Can anybody help? Because I can't find the answere anywhere.

And I think that definition, like, f is diferentiable(continuos) in domain (a;b) if it is diferentiable in all the particular points, doesn't work for me, because it is not possible to check all the points.