a) Prove from definition that iff, g : R -->R are differentiable functions, then the product function fg is also differentiable.

(b) Prove that if h : R --->R is a differentiable function that satisties

|h(x)-h(y)|< or = |x-y|^1.5

for all x; y elements of R, then h(x)=0 for all x.

(c) Give an example of a function k : R --->R such that k is differentiable but not twice differentiable.