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I am currently taking a numerical analysis course, whose main reference is the book "Numerical Analysis" by Richard L. Burden and J. Douglas Faires

I am preparing for a presentation about numerical differentiation. One of the main reference is the section 4.1 of the prementioned book. The authors did mention about 2-points, 3-points and 5-points formulae used to approximate derivatives. However, I still have no idea why they didn't mention 4-points formulae. These are also a special case of the general $(n+1)-$point formula. Why aren't they mentioning about them? Is it because that the 4-points formulae can't be applied as well as the 2,3 and 5 do?

Any help is properly appreciated.

ElementX
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    It would be good to add which derivatives you are trying to approximate. Is it $f'$ or higher order derivatives. Confirm if you step size is uniform. – Carl Christian May 09 '18 at 14:52
  • This text: http://fac.ksu.edu.sa/sites/default/files/textbook-9th_edition.pdf – Mason May 09 '18 at 15:14
  • It looks to me like the n+1 case is given so that you can derive any you'd like. And then they give 2 examples. – Mason May 09 '18 at 15:15
  • Or are you saying that they don't mention the n+1 case? – Mason May 09 '18 at 15:19
  • It's given on page 176. Equation 4.2 – Mason May 09 '18 at 15:20
  • I'm trying to approximate the first derivative. I'm talking about the case where $n = 3$ (4 points formulae). The authors didn't mention about them in the textbook. I'm wondering if there is a particular reason – ElementX May 09 '18 at 15:41

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