Define h : R - R by

h(x) = {x^2, x rational

h(x) = {0, x irrational

1. Prove that h is dierentiable at 0.

2. Prove that h is not continuous at c not = 0. You may use the fact that any

interval in R contains both rational and irrational points.

(Hint: Split the proof into two cases: one for c rational, the other for c irrational.)

3. Prove that h' is a function whose domain is {0} and that h" does not

exist.