## Section 10.1 - Limits & Motion: The Tangent Problem

**Essential Question(s):**

Explain the distinction between an average velocity and an instantaneous velocity.

**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.

__Average Velocity__

- What is average velocity? (pg 792)
- How do you compute average velocity? (Ex 1 pg 792)

__Instantaneous Velocity__

- What is instantaneous velocity? (pg 792 - 793)

__Limits Revisited__

- What is the informal definition of a limit at a? (pg 794 & read paragraph above box)
- How do you use limits for instantaneous velocity? (Ex 2 pg 794)

__The Connection to Tangent Lines__

- Why was a tangent line introduced when finding instantaneous velocity? (pg 795)
- How do you find the slope of a tangent line? (Ex 3 pg 796)

__The Derivative__

- What is the definition of the average rate of change? (pg 796)
- What is the definition of the derivative at a point? (pg 797)
- What is another version of the definition of the derivative at a point? (pg 797)
- When can the derivative not exist? (bottom of pg 797; graphs)
- How do you find the derivative at a point? (Ex 4 pg 798)
- What is the definition of the derivative of a function? (pg 798)
- What is Leibniz notation? (pg 798)
- How do you find the derivative of a function? (Ex 5 pg 798)-799)

**STEP 3: Reading**

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

- Read pages 792 - 799.
- Make sure to read the paragraphs between the examples.