Given three equally-spaced points, we can find an interpolating polynomial passing through those points, find the derivative, and evaluate the derivative at the midpoint to get a good approximation of the derivative at the midpoint.

# Background

Useful background for this topic includes:

# References

- Bradie, Section 6.2, Numerical Differentiation, Part II, p.438.
- Mathews, Section 6.1, Approximating the Derivative, p.321.
- Chapra, Section 23.1, High-accuracy Differentiation Formaulas, p.632.

# Interactive Maplet

To generate a centred divided-difference formula, keep the points centred around *x*, for example, `f(x - 3*h)` to `f(x + 3*h)`.

# Interactive Maplet

To generate centred divided-difference formula, keep the points centred around *x*, for example, `f(x - 3*h)` to `f(x + 3*h)`.

Copyright ©2005 by Douglas Wilhelm Harder. All rights reserved.