Continuity and Differentiability from a Real Analysis Standpoint

Question

Let f_a(x) = {x^a if x > 0

{0 if x <= 0

a) For which values of a is f continuous at 0?

b) For which values of a is f differentiable at 0? Is the derivative function continuous?

c) For which values of a is f twice-differentiable?

Answer 1

a) a > 0

b) a>1, yes

c) a > 2