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Derive using Taylor series/Establish error term

  1. Feb 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Derive the following formula using Taylor series and then establish the error terms for each.

    2. Relevant equations

    f ' (x) ≈ (1/2*h) [4*f(x + h) - 3*f(x) - f(x+2h)]

    3. The attempt at a solution

    I honestly have no idea how to go about deriving this. The professor did not require a book for this class, and he never did an example. Any help would be greatly appreciated.
  2. jcsd
  3. Feb 24, 2012 #2

    Ray Vickson

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    Do you know what a Taylor series is? If so, apply it to f(x+h) and f(x+2h), keeping just a few terms in each expansion.

  4. Feb 24, 2012 #3
    Honestly, it's been several years since I've worked with Taylor series. The class is Numeral Methods. I'm confused by how the formula is set up. Everything I've looked up online does not look like this at all.
  5. Feb 25, 2012 #4
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