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.