Hi! I'm not sure if this is the correct forum to ask this question but here it is.

I'm asked to give a formula for the (unique) polynomial K_{3n+2}(x) of degree at most 3n+2 such that

K_{3n+2}(x_{j}) = f(x_{j}), K^\prime_{3n+2}(x_{j}) = f^\prime(x_{j}),  K''_{3n+2}(x_{j}) = f''(x_{j})

for j=0,...,n.

Also, it is assumed that

f \in C^2[a,b] Where C^2 is the set of all functions having it's 2nd continuous derivatives on [a,b].

Let  a=x_{0} < x_{1} < ... < x_{n} = b

and

Let 3n+3 values

f(x_{0}), f(x_{1}), ..., f(x_{n})

f'(x_{0}), f'(x_{1}), ..., f'(x_{n})

f''(x_{0}), f''(x_{1}), ..., f''(x_{n})

be given.


This is all i have?!? I want to do this with Maple using either Lagrange or Neville's interpolation but I have no clue where to start. Any help would be greatly appreciated.