the formulea for calculating derivatives of different error orders

Sorry to misuse issues to ask questions, but I could't find any other way to communicate with you developers.
I am using this package to calculate the first order derivative of a matrix which can be thought of a function of mono variable x, i.e., M(x). I find that the derivative is hard to converge. By converging I mean if I add more nodes when calculating the derivative, the derivative is unchanged under some tolerance. In practice, I just increase q in central_fdm(q, 1).
I have tried q up to 12 but the result didn't seem to convergence. I couldn't increse the order any more because the time for calculation is unacceptable in my case.
I also tried to change max_range, and the result is quite different from that calculated with default max_range.
That led me to investigate the details of calculating method of FiniteDifferences.jl. I found that the method for calculating derivative in this package is not that easy to understand, especially I find that it choose nodes of two different set.(see picture below)

So would you please give some more details on how the nodes are chosen, especially the meaning of max_range and how are the derivatives calculated using the nodes?

Start by reading the implementation and documentation for central_fdm(q, 1), focusing on how max_range and the two node sets are described. Compare that explanation with the reported matrix-derivative convergence behavior. Done means documenting how nodes are chosen, what max_range means, and how the derivative is calculated, with the behavior clearly explained to users.