Instantaneous Rate of Change: Exploring More Functions with the First and Second 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 shows the instantaneous rate of change for different values for polynomial functions of degree 2, 3, or 4, an exponential function, and a logistic function.

[more]

Do some experiments:

Choose the logistic function. Check the first derivative box. Find an approximate value where the increase of is highest.

Choose the exponential function. Check the second derivative box. Find an approximate , the inflection point, where the tangent line switches from above the function to below. Actually, it is the zero of .

Choose the polynomial of degree four. Check both the first derivative and second derivative boxes.

How big is when has its local maximum and local minimum?

[less]

Contributed by: Wolfgang Narrath and Reinhard Simonovits (September 2007)
Open content licensed under CC BY-NC-SA


Snapshots


Details



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.
Send