(1) Let

(a) For which of the values of is continuous at zero?

(b) For which values of is differentiable at zero? In this case, is the derivative function continuous?

(c) For which values of is twice-differentiable?

(2) Let and be functions defined on an interval , and assume both are differentiable at some point

Prove the following:

(a)

(b) for all (R is the reals)

Any help would be greatly appreciated, thanks!