Pathological Derivatives

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration explores how the definition of a derivative plays out for some pathological functions. By changing , you can see that in most of the examples, the slopes of the secant lines do not have a finite limit as . An interesting comparison, however, is one between the continuous extensions of and ; both are continuous with oscillatory behavior, but only the latter is differentiable at .

Contributed by: Stepan Paul (June 2015)
Open content licensed under CC BY-NC-SA




Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.