Lesson #65


Quote of the Day:
"Mathematics, rightly viewed, possesses not only truth, but supreme 
      beauty." -- Bertrand Russell

Objectives:
The student will intuitively learn about decreasing and increasing 
   functions.
The student will intuitively learn about concavity and points of 
   inflection.

1. Hand back test on Chapter 4.

2. Today we will try to come to an intuitive understanding
   of the following concepts:
	(A) increasing function
	(B) decreasing function
	(C) constant function
	(D) concave up
	(E) concave down
	(E) point of inflection

3. Draw a curve on the blackboard and discuss topics above:

       

4. When is the function increasing?
        
          

     If f'(x) > 0    Then f(x) is increasing.
     If f'(x) < 0    Then f(x) is decreasing.
     If f'(x) = 0    Then f(x) is constant.

5. Examples:
     Find the intervals where each of the following 
     functions are increasing and decreasing:
        

6. Example of function: Calculus for all seasons
           Click here for Calculus for all Seasons

7. Assignment: 
          p. 275 (1, 2, 3, 7)
Lesson #65 Increasing and Decreasing Functions

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