## Section 4.3 - 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__

__Concavity__

- What is concavity?
- What is the concavity test?

__Points of Inflection__

- What is a point of inflection?
- What are some cautions when using the second derivative for points of inflection?

Second Derivative Test for Local Extrema

Second Derivative Test for Local Extrema

- What is the second derivative test for local extrema?

__Learning About Functions from Derivative__

- Summary of what we can learn from first and second derivatives.

**STEP 3: Reading**

__If time permits, reread__the lesson and take any extra notes as needed.