Question

Why would a polynomial function indicate that it's differentiable everywhere?

Answer 1

Why a polynomial is differentiable everywhere?
I guess this has something to do with the fact that
-a polynomial's domain is \(\large \mathbb{R}\)
-\(\large ax^n\) is differentiable for any real number a and positive integer n.

and of course, the fact that the sum of any finite number of differentiable functions is also differentiable :D