Summary

This graph image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}. It is recommended to name the SVG file “AbsoluteErrorNumericalDifferentiationExample.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.

Details

I made this using the graphics programming language TikZ, Beamer and LaTeX

The plot displays the absolute error when computing the derivative of ${\displaystyle f(x)=x^{3}}$ (${\displaystyle f'(x)=3x^{2}}$) using a forward difference (of first order) and a centered difference (of second order),

${\displaystyle {\frac {f(x+h)-f(x)}{h}}-3x^{2}}$

for various values of ${\displaystyle x}$. The centered difference is for ${\displaystyle x=0.1}$ only.

The noisy negative slope is due to finite precision (64-bit IEEE754) in the computer used, and the positive slope is due to the formula error of the differentiation formula.

Licensing

I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.