Math 122 Class Notes

Spring 2001

Class Date Notes
1/8 Discuss syllabus/expectations.   Begin discussing section 2.1.    Specifically  discuss average vs instanteous velocity (pages 88-90). Classwork  (Did exercises 1-3)
1/9 Completed excercises 4-6 on classwork above.  Discussed the definition of instanteous velocity.  Discussed what it means for average velocity to be negative, positive, zero.  
1/10 Answered questions on hw solutions.  Discussed relationship between the slope of a secant line on the graph of a position function and average velocity as well as the relationship between the slope of a tangent line and instantaneous velocity.
   
   
Illustration of tangent line as limit of secant lines:

http://www.math.psu.edu/dna/graphics.html#secants

http://home.a-city.de/walter.fendt/me/sectang.htm 

 

   
   
1/24 Quiz (p. 111 #13); answered hw questions from 2.4; from 2.5 defined concavity:  f is concave up on an interval iff f ' is increasing on the interval.  f is concave down on an interval iff f ' is decreasing on the interval.  Illustrations.
1/29 Answered hw questions; discussed  (via p. 123 # 11) what it means for a function to be non-differentiable at a point; from section 2.5 discussed the equivalency of these statements:

f ' increasing on (a,b); f '' positive on (a,b); f concave up on (a,b)

f ' decreasing  on (a,b); f '' negative on (a,b);  f concave down on (a,b)

Last Updated on January 29, 2001

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