I've attached the problem typed up to be more clear. I'm basically having trouble on how to prove that g'(x) exists using only that I know that f(x)<=g(x)<=h(x) for some neighborhood around x_0. I'm pretty sure I have to use some definition of the differentiation, but can't quite prove to myself that it exists without having more information.

Any help would be appreciated.

Attachment 20905