## Section 2.4 - Rates of Change, Tangent Lines, and Sensitivity

**Essential Question(s):**

How are rates of change and tangent lines related?

**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 Rates of Change - REVIEW__

- What is the average rate of change? (pg 87)
- How to you compute average rate of change? (Ex 1 pg 87)
- How can you apply average rate of change? (Ex 2 pg 87-88)

__Tangent to a Curve__

- Why find tangents to curves? (sidebar pg 88)
- What is the general method of finding the tangent to a curve? (pg 88-89)
- REVIEW - How do you find the slope and tangent line to a curve at a specific point? (Ex 3 pg 89)

__Slope of a Curve__

- What is the slope of a curve at a point? (pg 89 figure 2.30, pg 90 definition)
- Exploring slope and tangent. (Ex 4 pg 90)
- These are all the same. (sidebar pg 90)
- What is the different quotient of f at a? (pg 90)

__Normal to a Curve__

- What is the normal line? (pg 91 & sidebar)
- How do you find a normal line? (Ex 5 pg 91)

__Speed Revisited__

- What is the instantaneous rate of change of position with respect to time? (pg 91)
- REVIEW - How do you find instantaneous rate of change? (Ex 6 pg 91)
- How do you compute the speed of a free falling object? (Ex 7 pg 92)

**STEP 3: Reading**

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

- Read pages 87 - 93.
- Make sure to read the paragraphs between the examples and sidebar snippets.