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$f'(x) \thickapprox$ $\frac{1}{2h} [ 4f(x+h) - 3 f(x) + f(x + 2h)]$

I need to derive the approximation formula for the function above. And I need to show that it's error term is of the form $\frac{1}{3}h^2 f'''(\xi)$

How do I go around doing this? I've been suggested to use the Central Difference Formula or Forward or Backward Approximation

  • 3
    You'll have a tough time, since the formula is wrong, or not well written. Let $f(x)=x$. We get nowhere near $1$. But for example if you interchange $4$ and $3$, you get something more plausible.2012-01-31
  • 0
    I double checked, I have the correct formula2012-01-31
  • 3
    Do you mean (on top) $4f(x+h)-(3f(x)+f(x+2h))$? Please note the parentheses.2012-01-31
  • 0
    The way I wrote it in the question is how I it is written in the book that I have. It is apparently poorly written then2012-01-31

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