Calculus AB
Retention and Connection
To learn calculus well, it is wise to conduct periodic reviews. We need to (1) keep older concepts in
memory and (2) see how concepts are related.
Therefore, we will prepare 25 note cards summarizing Chapter 3. Then we will identify two concepts
from Chapter 2 that Chapter 3 has advanced and describe how our outlook on those concepts should have
evolved.
Note Cards
 Prepare a 3”x5” (the small size) card for each topic containing the following information
Front side
* A clear expression giving the rule or concept in correct mathematical notation/wording.
* If the rule has a name, that should be given (like product rule/quotient rule).
* A specific example/problem which you merely present on the front of the card.
Back side
* The solution to the problem you presented on the other side.
The Card Topics
1
Definition of the derivative
* give 3 forms
* use only one of them to find the derivative rule for y = 2x3 (do this on the back side)
2
Power rule
3
Product rule
4.
Quotient rule
5-10 Derivatives of all 6 trig functions
11
Chain rule
12
Parametric chain rule
13
Implicit differentiation
14-19 Derivatives of all 6 inverse trig functions
20-21 Derivatives of eu and au
22-23 Derivatives of ln (u) and logau
24
Derivatives of y = xx using logarithmic differentiation
Connections
1. On one additional 3x5 card discuss how the Chapter 2 concept of “tangent slope” evolved in Chapter 3.
Address the following points:
(a) What did tangent slope actually turn out to be?
(b) How does the meaning of the definition in the box on p. 90 differ from the meaning of the
definition in the box on p. 100?
2. On a second additional 3x5 card discuss the difference between “average rate of change” and
“instantaneous rate of change.” Address both graphical and function implications.
Scoring: 2 points for card #1 (2) + 1 per card #2-24 (23) + 2 points for each connections card (4) + 2
points neatness (1) = 30 points
Due Date :
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