Finite Difference Approximations of the First Derivative of a Function

Derivatives of functions can be approximated by finite difference formulas. In this Demonstration, we compare the various difference approximations with the exact value.

Both forward and backward difference formulas have error , while the central difference formula has error .

In this Demonstration, we show the difference in values calculated from the three difference formulas and the exact value.

Questions: 1. Does the true error increase proportionally with the step size, , for the forward and backward difference formulas? 2. Does the true error increase proportionally with the square of the step size, , for the central difference formula?