Use Taylor to derive a numerical differentiation formula of

Last updated: 7/12/2022

Use Taylor to derive a numerical differentiation formula of the form f (x) = Af(x) + Bf (x-h) + Cf (x-2h) (h>0) that has precision O(h) for f sufficiently regular. What is the required regularity for f? Check the accuracy by numerical experiments, one to show the performance and one to show the necessity of the specified regularity.