Family of Curves, Tangents, and Intuition

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.

Visualizing a family of curves can give an intuitive feeling for their properties, but sometimes that intuition is wrong. So it is helpful to be able to compute, check, and display results.


Each curve has a vertical tangent at , which comes from taking the limit. So there is no derivative at .

At , the curves with odd never have the same tangent and are never horizontal.

At , the curves with even alternate between having a derivative of and .

At , the curves with odd always have the same tangent. At (, 0), the curves with even always have the same tangent (different from the odd case).


Contributed by: Jacqueline Zizi (March 2011)
Additional contributions by: Michael Schreiber
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.