10182

# Instantaneous Rate of Change: Exploring More Functions

This Demonstration shows the instantaneous rate of change of for different values for polynomial functions of degree 2, 3, and 4, an exponential function, and a logistic function.
Choose the cubic polynomial for some experiments. Consider the red point and line. Move slowly from -1.17 to 3.9. What changes do you notice? Is there a relation? Write down your conclusion. Move slowly from -1.17 to 3.9 again. Make a table for the intervals in which is negative, zero, or positive.
What is the orientation of the tangent line (increasing, decreasing, horizontal) when is positive or negative?
What is the position of the tangent line if ?
How does change its sign around the local maximum? Around the local minimum? Moving the slider from left to right?
You found a relation between the value and the position of the tangent line.
Is this relationship also correct for the fourth-degree polynomial, the mixed exponential function , and the logistic function ?

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Curriculum Standards

US Common Core State Standards, Mathematics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.