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 $\displaystyle K_{3n+2}(x)$ of degree at most $\displaystyle 3n+2$ such that

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

for $\displaystyle j=0,...,n$.

Also, it is assumed that

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

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

and

Let $\displaystyle 3n+3$ values

$\displaystyle f(x_{0}), f(x_{1}), ..., f(x_{n})$

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

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

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.