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Homework Help: Interpolation, proving P[x_0,x_1, ,x_n] = 0

  1. Oct 31, 2013 #1
    1. The problem statement, all variables and given/known data
    I am asked to show that P[x0,x1,...,xn] = 0 for P(x) [itex]\in[/itex]∏n-1 without directly using the property that the divided difference
    over n+1 nodes is the nth derivative. The hint says to use the formula for the error.

    2. Relevant equations

    3. The attempt at a solution
    I am not quite sure how to approach this. I am familiar with the expression for the error. I am also familiar with Rolle's Theorem, or Mean Value Theorem, but am I allowed/supposed to use that based on the indications in the question?
    I'd appreciate some guidance. Thanks!
  2. jcsd
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