Calculators and numerical differentiation

[Paul Dale]

The WP 34S doesn't use either of the methods discussed. It uses an order 10 method for it's derivative with fallbacks to order 6 and 4 if the function doesn't evaluate properly. For the second derivative is again uses an order 10 method with a fallback to an order 4 method. The order 10 methods are a weighted summation of \( f(x \pm 1) \), \( f(x \pm 2) \), \( f(x \pm 3) \), \( f(x \pm 4) \) and \( f(x \pm 5) \).

There are good reasons for not wanting to evaluate the function at the x specified.