Mr. Daniel J. Lynch
AP Calculus AB
§3.1 Reading Assignment
1. Define the meaning of Extrema “in your own words”.
2. Do the Exploration at the bottom of page 164. Use your calculator to check your work.
3. Write out Example 1.
4. What is a critical number? Please define “in your own words”.
5. What are the guidelines for finding Extrema on a closed interval?
6. Write out Example 3.
Mr. Daniel J. Lynch
AP Calculus AB
§3.2 Reading Assignment
1. Do the Exploration: Extreme Values in a Closed Interval – p. 172
2. Who was Michel Rolle?
3. Copy Rolle’s Theorem and use Figure 3.8 to verify this theorem.
4. Do the Technology Pitfall (bottom of p. 173).
5. What is the Mean Value Theorem? Use Figure 3.12 to verify.
6. Write out Example 4.
7. What is the Alternative Form of the Mean Value Theorem?
Mr. Daniel J. Lynch
AP Calculus AB
§3.3 Reading Assignment
1. “In your own words” define Increasing and Decreasing Functions. How would you test for this?
2. What are the guidelines for finding intervals on which a function is increasing or decreasing?
3. What does strictly monotonic mean? Refer to Figure 3.17.
4. Write out The First Derivative Test.
5. Copy Example 2, then do the Exploration at the bottom of p. 182.
6. Do the Technology Pitfall on p. 182. Copy the graphs and results.
7. Copy Example 4, along with Figure 3.22.
Mr. Daniel J. Lynch
AP Calculus AB
§3.4 Reading Assignment
1. Define concavity by using Figure 3.24.
2. How do you test of concavity?
3. What are points of inflection and how do you find them? Use Figure 3.28.
4. Write out Example 3.
5. What is the Second Derivative Test? Try to explain “in your own words”.
6. Write out Example 4.
Mr. Daniel J. Lynch
AP Calculus AB
§3.5 Reading Assignment
1. Use Figure 3.33 to define “end behavior” and Limits at Infinity.
2. What is a Horizontal Asymptote?
3. “In your own words” define the theorem for Limits at Infinity (p.199).
4. Write out Example 3.
5. What are the Guidelines for Finding Limits at Infinite of Rational Functions?
6. List all Indeterminate forms (p.567-573).
7. What is the “Witch of Agnesi”?
8. Do the Technology Pitfall as the bottom of p. 202. Use Figure 3.39.
9. Write out Example 5.
10. What are Infinite Limits at Infinity?
Mr. Daniel J. Lynch
AP Calculus AB
§3.6 Reading Assignment
1. What are the Guidelines for Analyzing the Graph of a Function?
2. Copy down Example 1.
3. Do the Technology Pitfall at the bottom of p. 211. Describe your findings.
4. Write down Example 3.
5. Write down Example 5.
6. Summarize the paragraph at the bottom of p. 213.
Mr. Daniel J. Lynch
AP Calculus AB
§3.7 Reading Assignment – Optimization Problems
1. Other than the examples listed at the top of p. 218, what are some frequent terms you have heard or read that you would need to optimize? Please list a few.
2. Write out Example 1.
3. Now, verify your results from Example 1 by using a graphing calculator. Please sketch the viewing window and locate the maximum value of V on your graph.
4. What are the guidelines for solving applied minimum and maximum problems?
5. Write out Example 2.
6. Write out Example 5. “An Endpoint Maximum”
7. What is one of the main goals of this course?
Mr. Daniel J. Lynch
AP Calculus AB
§3.9 Reading Assignment - Differentials
1. What is the Tangent Line Approximation of f at c?
2. Do the Tangent Line Approximation Exploration on page 235. Draw this representation and answer the questions.
3. Write out Example 1and Figure 3.65.
4. Explain the definition of Differentials in your own words.
5. Explain propagated error in your own words.
6. Copy down table of Differential Formula Table.
7. Write out Example 4.
8. What is the Leibniz Notation? Who is Leibniz (other than “The Man!”)?
9.Write out Example 6.