Approximating function derivatives

[Namir]

Albert,

I translated your last pseudo-code into Excel VBA. The code works well and gives accurate results With x0 = 6, the code takes 8 iterations (like my Newto'ns version).

The real savings in function callis adapting your fx averaging approach to Halley's method. This way the fx averaging approach will use two function calls per iteration as opposed to 3 function calls when I calculate f(x), f(x+h) and f(x-h).

Namir