Assignment 8: Rules for Calculating Derivatives

Week 9

In class on Monday, [day 23]:

·        Section 4.4: The Product Rule

·        Working with functions visually

o       Where are the zeros of each function? 

o       Where are the slopes of each function positive / negative?

o       One of these two functions is the derivative of the other.  Which is the original function, which is the derivative?  How do you decide this?

In class on Wednesday, [day 24]:

·        Section 4.5: The Chain Rule

·        Working with functions visually

o       Use your CAS to graph the function and its derivative. 

o       From the graph, estimate the zeros of the function, and the zeros of the derivative.

o       Where are the slopes of the original function positive / negative?

o       What can you say about the derivative when the slope of the function is positive? 

o       Where does the function take on local maxima or local minima? 

o       What is happening to the derivative at these points?

o       Where is the derivative equal to zero? What is happening to the function at these points?

o       Where does the derivative take on local maxima or local minima?

o       What is happening to the function at these points?

o       On which regions is the graph of the original function concave up / concave down?

o       From the graph, estimate the points where the function changes from concave up to concave down.  What is happening to the derivative at these points?

In class on Friday, [day 25]:

·        Section 4.6 Derivatives of Functions Defined Implicitly

·        Project 2: Air Traffic Control

This project is presented at the end of this chapter (Project 1: Air Traffic Control).  Specific project requirements will be available as a separate handout.  This project will be due at the beginning of class on Monday, November 2.  You will have some time to work with your group on this project in class on Monday, October 26.  You may need to work outside of class to complete this project. 

o       We will work on Exercises from Sections 4.4, 4.5, and 4.6.  You will have an opportunity to put some of your work for these exercises on the board.  (Hint: These exercises make good test questions!)