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Homework Help: Basis functions for polynomial

  1. Sep 10, 2010 #1
    1. The problem statement, all variables and given/known data
    For I = [a,b], define: P3(I) = {v: v is a polynomial of degree ≤ 3 on I, i.e., v has the form v(x) = a3x3 + a2x2 + a1x + a0}. How to show v is uniquely determined by v(a), v'(a), v(b), v'(b).

    2. Relevant equations

    3. The attempt at a solution

    I'm not exactly sure what I'm being asked to do here. I don't need the problem solved, just a nudge in the right direction.
  2. jcsd
  3. Sep 10, 2010 #2


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    Homework Helper
    Gold Member

    I guess I = [a,b] just stands for an interval of real numbers?

    I also guess that you are allowed to assume that multiplication and addition of given real numbers always produces a unique real number?

    Then your four given coefficients ai uniquely determine P.

    So it seems you are being asked to prove that v(a), v'(a) etc. uniquely determine the ai .
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