## Section 3.1 - Derivative of a Function

**Essential Question(s):**

How are derivatives related to rates of change?

What are the graphical connections between functions and their derivative?

**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.

__Definition of Derivative__

- What is the derivative of f at a? (pg 101)
- What is the derivative? (definition pg 101)
- What is a differentiable function? (pg 101)
- How do you apply the definition of a derivative? (Ex 1 pg 101-102)
- What is the alternate definition of a derivative? (pg 102)
- How do you apply the alternate derivative definition? (Ex 2 pg 102)

Notation

Notation

- What are the many notations for derivatives? (pg 103)

Relationships Between the Graphs of f and f'

Relationships Between the Graphs of f and f'

- What is a relationship between the graphs of f and f'? (pg 103)
- Go through example 3 and take notes as needed. (pg 103-104)
- How can you graph f from f'? (Ex 4 pg 104)

One-Sided Derivatives

One-Sided Derivatives

- What are the characteristics of one-sided derivatives? (pg 106)
- How can one-sided derivatives differ at a point? (Ex 6 pg 106)

**STEP 3: Reading**

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

- Read pages 101 - 106.
- Make sure to read the paragraphs between the examples and sidebar snippets.