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What is the relationship between finite differences and the leading coefficients?

  1. May 10, 2008 #1
    1. The problem statement, all variables and given/known data
    Determine the relation that exists between the nth finite difference and the leading coefficient.



    2. Relevant equations
    ... I'm not too sure how to html it up properly, but the numbers/"n"s following the "a"s are meant to be sub-script:
    f(x) = anx^n + an-1x^n-1 + ... + a2x^2 + a1x + a0


    3. The attempt at a solution
    If someone could even tell me the proper direction for the line of thought here. All I can figure out thus far is that the difference is the same sign (positive or negative) of the coefficient. Any hints would be GREATLY appreciated!!!!

    Thanks!
    ~D
     
    Last edited: May 10, 2008
  2. jcsd
  3. May 11, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Are you assuming an nth degree polynomial?

    Try some easy cases first. What is the first difference of ax+ b?
    What is the second difference of ax^2+ bx+ c?
    What is the third difference of ax^3+ bx^2+ cx+ d?
     
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