Thread: Finite differences and polynomials

I've been having some difficulty understanding finitite differences and their relation to polynomials. Would someone be able to give me a brief overview? Also maybe explain how i could answer this question

Explain how to use finite differences to see if a set of data can be modelled using linear, quadratic, cubic, or quartic polynomial functions.

Thanks in advance.

Originally Posted by Dalet

I've been having some difficulty understanding finitite differences and their relation to polynomials. Would someone be able to give me a brief overview? Also maybe explain how i could answer this question

Explain how to use finite differences to see if a set of data can be modelled using linear, quadratic, cubic, or quartic polynomial functions.

Thanks in advance.

A sequence of points is a polynomial if and only if after a certain amount of finite differences it becomes constant.

Thus, for example,
1,2,3,4,5,6,...
The finite difference is,
1,1,1,1,1,...
It is constant, thus there exists a polynomial that defines it.

Furthermore, the number of finite differences that we made were 1. In this case the polynomial is a polynomial of degree 1.