This is the question I have
Let f(x) be a given function which can be evaluated at any point. In the following question, h refers to the step size or the distance between the equally spaced points used in the approximation.
Find a 2nd order method (i.e., truncation error O(h2)) approximating
Give the formula as well as an expression for the truncation error. Hint: You may want to consider the Taylor expansions of f(x0 ±h) then f(x0 ±2h). It is easier to consider each of these cases separately, then combine the results.
I'm just looking for a start or some sort of M-file to get me going on the rest of the stuff. I know the taylor expansions for f(x+h),f(x-h),f(x+2h),f(x-2h) but im not sure how to comebine them to make this work. I know I have to get this and then plug different h's in to see the difference in error.
Thank you very much.