## Section 5.3 - Connecting f' and f'' with the Graph of f

**Essential Question(s):**

Explain how the first and second derivatives are used to analyze the behavior of a function.

**Follow**__these three steps__to complete this "flip" lesson.**STEP 1: Preparation**

__Title__your spiral with the heading above and

__copy__the essential question(s).

**STEP 2: Vocabulary & Examples**

__Copy__and

__define__the following of vocabulary. This can be any tables, properties, theorems, terms, phrases or postulates listed.

__Review__the following examples and

__copy__what is necessary for you. Use the guiding questions for your Cornell notes.

__First Derivative Test for Local Extrema__

- How does the first derivative determine local extrema? (Theorem 4 pg 211-212)
- How do you apply the first derivative test? (Ex 1 pg 212-213)

__Concavity__

- What is concavity? (pg 213)
- What is the concavity test? (pg 214)
- How do you determine concavity? (Ex 2 pg 214)

__Points of Inflection__

- What is a point of inflection? (pg 214)
- How do you find points of inflection? (Ex 3 pg 214)
- How do you read the graph of a derivative? (Ex 4 pg 215)
- Read the cautions of using the second derivative for points of inflection. Take notes as needed. (pg 215)
- How do you study motion along a line? (Ex 5 pg 216)

__Second Derivative Test for Local Extrema__

- What is the second derivative test and its tips? (Thm 5 and below pg 217)
- How do you apply the second derivative test? (Ex 6 pg 217)
- How do you apply f' and f'' to graph f? (Ex 7 pg 217 - 218)

__Learning About Functions from Derivative__

- Summary of what we can learn from first and second derivatives. (paragraph and table pg 218)
- How does a noncontinuous graph of f' lead to a continuous graph of f? (Ex 8 pg 219)

**STEP 3: Reading**

__Read__the following page(s) and take any extra notes as needed.

- Read pages 211 - 219.
- Make sure to read the paragraphs between the examples and sidebar snippets.