Let

be the collection of all functions whose domain is

and differentiable on the domain. Also, let

be the

collection of all functions whose domain is

and continuous on the domain.

I know that I need to

prove for any

,

for some

but I dont know how to go about writing the proof. Can anyone help me at least get a start on it? I'm sure I can figure it out with the proper hint.

Also, every example I find online, has

equaling some function (i.e.

). In my case, I dont have a specific function so that is why I am stuck and confused.