Define a function $\displaystyle h : \mathbb{R} \rightarrow \mathbb{R}$ by:

(THIS IS A PIECEWISE FUNCTION):

h(x) = {0 if $\displaystyle x \in \mathbb{Q}$ .. x^3 + 3x^2 if $\displaystyle x \not\in \mathbb{Q}$

1.) Determine which points h is continuous at, and determine which points h is discontinuous at. Prove these results.

2.) Determine which points h is differentiable at, and determine which points h is non-differentiable at. Prove these results.