Download III - Net Start Class

III.
“Applications of Differentiation” BC. Chapter 3. 20 days.
A.
Topics.
B.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Definition of Extrema on an Interval
Relative Extrema and Critical Numbers
The Extreme Value Theorem
Increasing and Decreasing Functions
The First Derivative Line Test
Rolle’s Theorem; The Mean Value Theorem
Concavity
The Second Derivative Test; The Second Derivative Line Test
Inflection Points
Monotonic Functions
Horizontal Asymptote Test
12.
L’Hopital’s Rule of the form
13.
14.
15.
16.
17.
18.
Curve Sketching Recipe
Optimization
Newton’s Method
Differentials
Linear and Quadratic Approximations
Motion Along a Line
0 
, .
0 
Teaching Methods and Evaluations.
1.
Each topic presented through lecture, student and group interaction,
2.
3.
4.
5.
6.
7.
8.
9.
graphing calculator usage, projects, supplements, Power Point
presentations, and assignments where applicable.
First Derivative Test project - discussion of the sign of the first derivative
and the increasing or decreasing behavior of the function. Student must
present the analysis through written sentences.
Second Derivative Test project - discussion of the sign of the second
derivative and the concavity of the function. Student must present the
analysis through written sentences.
Mean Value Theorem and Rolle’s theorem applications discussed
through interaction with supplementary AP material.
Function vs. its first and second derivative to discuss rate of change.
Student must present the analysis through written sentences; and
compare and contrast the function and its first and second derivative
through tables and graphs.
Intermediate Value Theorem and Extreme Value Theorem illustrated
graphically with discussion of continuity.
Regression Analysis to develop a model of the data, then graph its first
and/or second derivatives to discuss trends and make conclusions
algebraically, orally, and in written sentences.
Curve Sketching Project. Students present the graphing of functions
algebraically and in written sentences.
Optimization-problems related to engineering and business. Problems
are developed orally, algebraically, and with the use of the graphing
calculator to develop an applied use of the first and second derivative
tests.
10.
11.
Newton’s Method project. A student group project to develop the
solution to the zeros of a function and the comparison of the zero of the
tangent line to the zero of the function.
Supplements of Chapter 3:
a.
b.
c.
d.
e.
f.
g.
h.
13.
Evaluations.
a.
b.
C.
Review of solving Trigonometric Equations.
Curve Sketching outline with theorems and definitions. Curve
Sketching Recipe for successful Curve Sketching.
Curve Sketching project. Curve Sketching without the use of a
graphing calculator. Use all the techniques of curve sketching.
Continuous and Discontinuous functions, horizontal asymptotes,
vertical asymptotes, oblique asymptotes, and points where the function
is not differentiable are included. Graphing calculator used as
reinforcement.
Differentials to find Relative error and Percent area. Differentials
discussed and illustrated as an introduction to Integration, and its role
in Linear Approximation and Euler.
Applications with Linear Approximations and Quadratic
Approximations.
Applications for Motion Along a Line.
Use of AP Test Preparation questions of section XI to provide:
1.
Problems of distance, displacement, average velocity, and
instantaneous velocity,
2.
Reading graphs and tables to answer questions concerning
extrema, inflection, and concavity.
3.
Graphs of the first or second derivative, answer questions
concerning the function, f(x).
4.
Compare and Contrast the function, its first derivative and its
second derivative with graphs and tables.
5.
Tables to answer questions concerning average rate of change
and instantaneous rate of change.
6.
Questions using the alternate form of the derivative, first
derivative test, and the equation of the line tangent to the
graph.
Using tables, answer questions concerning average rate of change and
instantaneous rate of change.
Teacher created individual and group tests and evaluations.
Multiple Choice and Free Response questions of the College Board
and Fast Track to a 5 listed in XI of the syllabus.
Assignments.
Text: Larson, Ron., Edwards, Bruce and Robert P. Hostetler. Calculus. Boston:
Houghton Mifflin, 2006.
1.
2.
3.
4.
5.
6.
7.
3.1: Extrema. 5, 7, 15, 17, 25, 29, 31, 35 53, 55-58. *E: 69. Supplements.
3.2: Rolle’s and Mean Value Theorems. 7, 11, 17, 21, 25-45o, 49, 51, 57. *E:
65 67, 68. Supplements.
3.3: Increasing and Decreasing Functions. 9, 13, 15, 21, 27, 35, 39, 41,45, 49,
53, 55-71, 73. E:83, 7, 89, 91, 93. Supplements.
3.4: Concavity and the Second Derivative Test. 9, 17, 19, 25, 31, 37, 39, 41, 4547, 49-57, 61, 67, 71, 73. *E: 78. Supplements.
3.5: Limits at Infinity 5, 19, 25, 29, 31, 33, 37, 49, 51, 53, 59, 65, 69.
Supplements.
3.6: Curve Sketching. 1-6, 7, 13, 17, 19, 23, 29, 35, 37, 41, 47-53, 55, 61, 63,
67, 77. E: 78. Supplement.
3.7: Optimization. 3-19o, 23, 24, 25-29o, 33,49,51. *E: 65, 66, Section Project.
Supplement.
8.
9.
10.
11.
12.
13.
3.8: Newton’s Method. 1, 7, 11, 13, 15, 17, 21, 23, 33, 35, 37. Supplements.
3.9: Differentials. 3, 5, 9, 13, 15, 17, 21-35o, 43, 49, 51. Supplements.
Linear and Quadratic Approximations. Supplement. \
Selected problems of AP Test Preparation of section XI.
Fast Track to 5.
AP Free Response.
“We are what we repeatedly do. Excellence, then, is not an act, but a habit…” Aristotle.
Parents and Students: Applications of Derivatives Unit Grading.
Major grades: (70%)
Daily grades: (20%). Fast Track; Class Presentations; Supplements; in
Class Activities; Quizes; Free Response; Group work.
Homework grades: (10%). Assignments. (view Calendar)
Parents and students are to be aware that the student receives use of a
solution key to the homework exercises and receives solutions to all
supplements in class.
Grade Sheets issued 2 times per 6 weeks. Gradespeed is updated within 48
hours of an assignment and or test.
Teacher Website updated per week. Calendar of pace on the website/Calendar.
Teacher Contact: [email protected] Use email, NOT Voice Mail please.
Student Signature:
________________________________
Parent Signature:
________________________________