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.

Tuesday or Thursday Afternoon Office Time (2:30pm - 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 10th	Oct 11^th	Oct 12^th	Oct 13^th	Oct 14^th
Unit 3 Packet PDF Version
AP Calculus AB Topic/Concept	Workday	Related Rates	Related Rates ACT Testing Day	New Unit Test 2	1^st & 2^nd Derivative Tests
Week 7					Quiz # 1 moved to Monday due to Pep Rally Schedule on Friday
2^nd & 3^rd Period		1. Discuss AP Calculus Exam Format, Cheating, Stealing, & Trust 2. Discuss HW 14 - Intro to Related Rates & Commercial for Related Rates 3. (Chant Process = "Picture Set-up Work Answer" "Macbeth Chant" 4. Related Rates Video Discovery Activity w/Index Card - 5 min 5. Discuss Related Rates Lego Career Project Information 6. Related Rates PPT	1. Finish Related Rates PPT Word Problems 2. Related Rates - Ruler Activity 3. Youtube - Related Rates Song 4. Read 4.3 & 4.6 5. Lego Career Project Plan Time related to National Events from Units 1, 2, or 3 - State the Specific Day and the National Event(s) used for each Word Problem. 6. Work on HW	New Unit Test 2 (60 min Time Limit) Lego Career Project Plan Time	1. Discuss National Events, Tues' HW, Wed's HW, & # 51 - "Distance, Velocity, & Acceleration" Song 2. Derivative Test Vocabulary, PPT, & Guided Notes 3. Example problems from PPT 4. Your Turn! & Turn the Light On Activity
		HW 1 - Related Rates due Friday by 7am Career Interest Survey, 4 Letter Code, Group Member's Names, & Career Choice on the Lego Career Project by Thursday 7 am ACT Students = Ruler Activity Say Something Nice To Your Parents!!!	Lego Career Project - Upload due Oct 31^st by 7am - Top 10 Voting due Nov 3^rdby 7 am Assignment Related Rates 2^nd Period 3^rd Period "Big Ideas" Weekly Journal Entries due Oct 19^th	HW 3 - Worksheets due Mon by 7am Read 4.3 & 4.6 = Remaining Students	Thurs' HW Watch AP Central Videos
AP Calculus AB Songs		# 19 - "Calculus Is Cool"	Youtube - Related Rates Song		# 51 - "Distance, Velocity, & Acceleration" # 16 - Derivatives of Graphs
National Events	*October 10* Angel Food Cake Day Cake Decorating Day Handbag Day Metric Day Walk to a Park Day World Mental Health Day Columbus Day Kick Butt Day Online Bank Day Native American Day	*October 11* International Day of the Girl Child Sausage Pizza Day	*October 12* Farmer’s Day Freethought Day Gumbo Day Savings Day Bring Your Teddy Bear to Work/School Day Curves Day Emergency Nurse’s Day Fossil Day Stop Bullying Day Take Your Parents to Lunch Day	*October 13* Train Your Brain Day Yorkshire Pudding Day	*October 14* Be Bald and Be Free Day Dessert Day *October 15* Cheese Curd Day I Love Lucy Day Grouch Day Shawarma Day White Cane Safety Day Sweetest Day *October 16* Global Cat Day Dictionary Day Sports 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

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 - Vocabulary

AP Calculus AB - "Paul's Notes" - Website Link

Flash Card Review of Derivatives - Website Link

MVT Formula

Rolle's Theorem

Mean Value Theorem

Extra Math Help

AP Central Video Resources
AP Central Login Code:

2^nd Period:

3^rd Period:

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!

Stay Safe, Do Your Best, Give Your Best,