Welcome to Unit 3 - Applications of Derivatives of AP Calculus AB

I will do my best to create a positive learning environment for each of you.
Most weeks we will utilize handfuls of technological tools.

Most Daily/ Weekly assignments will be due the next day.

Wednesday Afternoon Office Time (2:20pm - 3:00pm)

Be Your Best, Do Your Best, & Breathe!

Unit 3 Quote – “Believe in Yourself and all that you are. Know that there is something
inside you that is greater than any obstacle.” – Christian D. Larson

Unit 3 - AP Calculus National Objectives

Students will be able to use techniques of differentiation to:

Determine the applicability of important calculus theorems using continuity. (Intermediate Value Theorem, Rolle's Theorem, the Extreme Value Theorem, and the Mean Value Theorem)
Analyze properties of a function - 1^st & 2^nd Derivative Tests of a function can provide information about the function and its graph including intervals of increase or decrease, local (relative) and global (absolute) extrema, intervals of upward or downward concavity, and points of inflection.
Interpret the meaning of a derivative within a problem.
Solve problems involving related rates, optimization, and rectilinear motion.
Solve problems involving rates of change in applied contexts.
Use differentiation rules to calculate derivatives (powers, products, quotients, trigonometric functions, trigonometric inverses, exponential , natural logarithmic, logarithmic functions, higher order derivatives, and inverse functions).

Oct 24^th

Oct 25^th

Oct 26^th

Oct 27^th

Oct 28^th

Unit 3 Packet

PDF Version

AP Calculus AB
Topic/Concept

Derivatives of Trig Inverses

AP Registration Meeting
2^nd 1/2 of Class

Derivatives of Trig Inverses

Theorems - Rolles, Mean Value (MVT), & Extreme Value (EVT)

L'Hopital's Rule &
Linearization

Quiz # 3

Week 9

2^nd & 3^rd Period

1. Discuss National Events, Practice Test, & Twinkle Song

2. Derivatives of Trig Inverses - PPT - Part 1

3. Youtube - Inverse Trig Derivative Examples

4. AP Registration Meeting
2^nd 1/2 of Class

5. Work on Lego Career Project due Oct 31^st

1. Discuss HW, Quiz # 2 results, & Finish Mon's Lesson - if needed.

2. PPT - Part 2 & "I'm Dreaming of a Right Angle"

3. In-class Link

4. Group Activity WP = Poster Paper/Markers - from Mon's Lesson

5. Art Field Trip Students see Ms. B.

1. Guided Notes on Theorem PPT

2. Calculus Songs -

#53 - Oh Calculus

# 17 - The Mean Value Theorem

3. Game = Relay Race = Board

Candy = Prizes

1. L'Hopital's Rule & Linearization PPT & Notes

2. Youtube - L'Hopital's Rule Song

3. In-Class Link

Quiz # 3

HW 10 - Derivatives of Trig Inverses = Volunteers &

Upload of work

2^nd Period Link

3^rd Period Link

8 Assignments

1.Derivatives of Inverse Trig Functions
- 2.Differentiating Functions - Errors
- 3.Justification w/1st Der Test
- 4.Justification w/ 2nd Der Test
- 5.Tangents to graphs of Implicit Relations
- 6.IVT & EVT Graph-
- 7.Justification w/IVT
-MVT
- 8.Using the MVT
Watch AP Central Videos

Read 3.9, 3.10, & Chapter 4 (Do Not Read Newton's Method)

Read Chapter 4
(Do Not Read Newton's Method)

Tue's HW due Friday by 7 am
Lego Career Project

HW 13 -due Monday by 7am
Read 3.9, 3.10, & Chapter 4 (Do Not Read Newton's Method)

Read Chapter 4
(Do Not Read Newton's Method)
Lego Career Project
Give A Small Gift To Someone!!!
"Big Ideas" Weekly Journal Entries

Lego Career Project due Oct 31^st
Practice Test
AP Central Problem Set # 3 due by 7 am Nov 8^th

AP Calculus AB Songs

#38 - Twinkle Writing

# 27 - You've Got A Plan

#33 I'm Dreaming of a Right Angle

#53 - Oh Calculus

# 17 - The Mean Value Theorem

# 81 - L'Hopital

#77 - L'Hopital

#36 - My Favorite Geometry Things

#36 - Mathematical Christmas Carol

Youtube - L'Hopital's Rule Song

National Events

October 24

October 25

Greasy Food Day

October 26

October 27

Black Cat Day

October 28

October 29

October 30

Candy Corn Day

Extra Practice:
- Related Rates Problems, if needed
- Theorem Review Worksheet - Do the Problems and then check your answers, if needed
- Related Rates -Shadow Example

- Optimization - Video Clip

Paul's Notes - AP Calculus AB - Website Link

Intermediate Value Theorem - Video Clip

Rolle's Theorem - VIdeo Clip

Mean Value Theorem #1 - Video Clip

Mean Value Theorem #2 - MVT

Extreme Value Theorem- Video Clip

L'Hopital's Rule Free Response Examples - Video Clip

1^st & 2^nd Derivative Test - Sentence Structure Notes

MVT Formula

Rolle's Theorem

Mean Value Theorem

Extra Math Help

AP Central Video Resources

3.1 The Chain Rule
3.2 Implicit Differentiation
3.3 Differentiating Inverse Functions
3.4 Differentiating Trig Functions
3.5 Selecting Procedures for Calculating Derivatives
3.6 Calculating Higher - Order Derivatives
4.1 Interpreting the Meaning of the Derivative in Context
4.2 Straight – Line Motion – Connecting Position, Velocity, & Acceleration
4.3 Rates of Change in Other Applied Contexts
4.4 Introduction to Related Rates
4.5 Solving Related Rates Problems
4.6 Approximating Values of a Function Using Local Linearity & Linearization
4.7 Using L’Hopital’s Rule for Finding Limits of Indeterminate Forms

5.5 Using the Candidates Tests to Determine Absolute Extrema

5.6 Determining Concavity of Functions over Their Domain

5.7 Using the 2^nd Derivative Test to Determine Extrema

5.8 Sketching Graphs of Functions and Their Derivatives

5.9 Connecting a Function, Its 1^st Derivative, and its 2^nd Derivative

5.10 Introduction to Optimization Problems

5.11 Solving Optimization Problems

5.12 Exploring Behaviors of Implicit Relations

Keep up the Good Work for this Semester in All of Your Classes!

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