Estimating f(2) using Cubic Interpolation

[escobar147]

If a cubic function satisfies f(0) = -32, f(1) = 0, f(3) = 10 and f(4) = 0,
use cubic interpolation to estimate f(2)



I'm not sure how to approach this since I have only ever done quadratic interpolation and linear interpolation, is it just an extension of the lagrange interpolating polynomial?

If so could someone please show me what form to put it in?

The correct answer is 12, however my attempt at extending lagrange give me nowhere near that?!

any help would be hugely appreciated!

 

[lanedance]

could you just start with g(x) = a+bx+cx^2+dx^3 and solve for the constants given the points you have?

 

[lurflurf]

There are many ways one of which being
$$P(x)=\sum_{i=1}^n \frac{\pi(x)}{\pi\prime(x_k)}\frac{f(x_i)}{x-x_i}$$
where in this case n=4 and
π(x)=(x-0)(x-1)(x-3)(x-4)
x₁=0;x₂=1;x₃=3;x₄=4