Are cubic hermite polynomials twice differentiable? If not, can you provide an example where this is the case, if n=2? More specifically, if given n=2 with {(x0,f(x0)),(x1,f(x1)),(x2,f(x2))}, H=H0 on [x0,x1] and H=H1 on [x1,x2], can you show H0''(x1)=H1''(x1)? H, H0 and H1 are all hermite polynomials.