Pathological Derivatives
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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
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"Pathological Derivatives"
http://demonstrations.wolfram.com/PathologicalDerivatives/
Wolfram Demonstrations Project
Published: June 9 2015