## Section 3.2 - Differentiability

**Essential Question(s):**

How are continuity and differentiability 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.

__How f'(a) Might Fail to Exist__

- When will f'(a) fail to exist? (pg 111)
- How do you find where a function is not differentiable? (Ex 1 pg 112)

__Differentiability Implies Local Linearity__

- What does locally linear mean? (pg 112)

__Numerical Derivatives on a Calculator__

- I will show you in class how to find derivatives, numerical derivatives and how to graph derivatives on your calculator.
- Make sure you read the "A word on notation" sidebar on page 113.

__Differentiability Implies Continuity__

- What is the connection between differentiability and continuity? (Theorem 1 pg 115)

__Intermediate Value Theorem for Derivatives__

- What is the Intermediate Value Theorem for Derivatives? (Theorem 2 pg 115)
- How do you apply the Intermediate Value Theorem for Derivatives? (Ex 5 pg 115)

**STEP 3: Reading**

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

- Read pages 111 - 115.
- Make sure to read the paragraphs between the examples and sidebar snippets.