# Homework Help: Cubic interpolation question

1. Oct 30, 2012

### 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!!!!

2. Oct 30, 2012

### lanedance

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

3. Oct 31, 2012

### 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