suppose that n \geq 1. The function f and its derivatives of order up to and including 2n+1 are continuous on [a,b]. The points x_i, i = 0,1,...n are distinct and lie in [a,b]. Construct polynomials r_0 (x), h_i (x), k_i(x) , i= 1,...,n of degree 2n such that the polynomial p_{2n} (x) = r_0 (x)f(x_0) + \sum_{i=1}^n h_i (x)f(x_i) + k_i (x)f ' (x_i) satisfies conditions p_{2n} (x_i) = f(x_i), i=0,1,...n and p ' _{2n} (x_i) = f ' (x_i), i=1,....n

I can't get anywhere with this. My professor doesn't teach examples, only theorems... help is much appreciated =)