Calculators and numerical differentiation

[Albert Chan]

(10-30-2020 09:57 PM)robve Wrote:  Came across this article that might be of interest to this forum: "calculators and numerical differentiation" http://blog.damnsoft.org/tag/fx-880p/

The author suggested Casio is doing central difference formula, based on Casio CFX-9×50 manual.
On closer reading, it only *illustrated* what is central difference.

Using the example f(x)=1/x, a = 0.001, h = 0.0001

f'(a) ≈ (f(a+h) - f(a-h)) / (2h) = -1/(a²-h²) < -1/a²

Casio fx-570MS: d/dx(1/x, 0.001, 0.0001) = -999974.6848 > -1/a²
Casio fx-115ES+: d/dx(1/x, 0.001) = -999999.999994767 > -1/a²

This suggested Casio is not using central difference formula as-is.
Something more is involved ...