Lesson #65
Increasing and
Decreasing Functions




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)

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Send any comments or questions to: David Pleacher