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Math Help - Finite differences and polynomials

  1. #1
    Dalet
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    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.
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  2. #2
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    Quote Originally Posted by Dalet View Post
    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.
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