Estimate Derivatives Given Function Values - Expii

Given a function f(x), you can estimate the derivative f'(a) numerically as the slope or difference quotient. This is basically an example of estimating limits numerically, since the derivative f'(a) is defined as a limit. In principle, as h approaches 0, the estimate will get better and better. In practice, calculators/computers are bad at dividing extremely small numbers (due to rounding errors), so you may need to be careful when h is too small.