Approximating function derivatives

[Albert Chan]

Hi, Namir

You could still do 2 function calls per Newton step, yet getting much better correction!

\(\displaystyle
\frac{f(x)}{f'(x)}
= \frac
{\frac{f(x+h) + f(x-h)}{2} + \mathcal{O}(h^2)}
{\frac{f(x+h) - f(x-h)}{2h} + \mathcal{O}(h^2)}
≈ \frac{f(x+h) + f(x-h)}{f(x+h) - f(x-h)} ×h
\)

see thread (HP71B) Newton's method