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2005 AP Calculus Syllabus - Chapter 5

Optimization & Applications of the Derivative
† (Building Calculus Muscles)

Mon., December 11: Section 5.1 Optimization Problems
        Introduction to Optimization Problems
            Session 1 – Notes – example 1 and 2
        Homework: Complete all six steps for each homework problem that you complete. Choose any 6 (at least 2 from each group) to complete from
        P. 308 #1-4, AND   p. 308 # 6-8, 10,    AND     P. 308 # 17, 19, 31, and 32

Tues,, December 12: Day 2 – example 3 and 4
Homework: Complete all six steps for each homework problem that you complete. Choose any 6 (at least at 2 from each group) to complete from
P. 308 # 5,11,13-15, AND p. 308 # 20-22, 30, AND p. 308 # 33-37

Wed., December 13: Day 3 – example 5
       Homework:   Complete all six steps for each homework problem that you complete.
       Choose any 6 (least 2 from each group) to complete from
       P. 308 # 9,16, 18, 23,    AND   24, 28, 29,    AND   38-50

Thurs., December 14: Section 5-2    Higher Order Derivatives
Objectives:
        * To use 1st and 2nd derivatives to measure velocity and acceleration
        * To use the graphs of derivatives to locate extrema and inflection points
        Homework: Read and take notes on P. 318 - 320 (2nd derivatives and acceleration) and do P. 326 # 21-28 using these NEW directions: locate where any extrema and inflection points are on the original function from the graphs of their derivatives) and do problems 35 - 38

Fri., December 15: Section 5-3    Implicit Differentiation and Inverse functions
Objectives:
        * To use derivatives to measure the slopes of more general curves than just function curves
        * To find derivatives of equations that cannot be simplified in terms of one variable using IMPLICIT differentiation
        * To apply the 3-step procedure to implicit differentiation
                1. assume that y is a differentiable function of x
                2. differentiate both sides of the equation with respect to x
                3. solve for dy/dx
        Homework: Read and take notes on p. 329 - 336 and review the IMPLICIT Differentiation Web page and do p. 339 #2-20 evens

Mon., December 18:     Section 5-3    Implicit Differentiation and Inverse Functions
Objectives:
        * To use implicit differentiation to find derivatives of inverses of functions
        Homework: P. 340 #22 - 32 evens and 33 - 46 all

Tues., December 19: Section 5-4:      Related Rates
Objectives:
        * To use the 5 step strategy to solve related rates problems
        Homework: Read and take notes on section 5 - 4 and do P. 347 # 1 - 14

Wed., December 20: Related Rates (cont.)
Objectives:
* To use the 5 step strategy to solve related rates problems
Homework: do P. 347 # 15 - 30

Thurs., December 21: Review - Quiz over chapter 5
        Homework:   Take Home Exam due Jan. 9 and Write one Jeopardy problem card for each of the following categories DUE Tomorrow
                1. Max/Min Problem
                2. Implicit Differentiation
                3. Position/Velocity/Acceleration Problem
                4. Related Rate Problem