Let g:R->R be a twice differentiable function satisfying g(0)=g'(0)=1 and g''(x)=g(x)=0 for all x in R.

(i) Prove g has derivatives of all orders.

(ii)Let x>0. Show that there exists a constant M>0 such that |g^n(Ax)|<=M for all n in N and A in (0,1).

Any help would be appreciated; not really sure where to start with this one.

OXF