## Section 2.2 - 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__

- What are four instances when f'(a) fail to exist?

__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.

__Differentiability Implies Continuity__

- What is the connection between differentiability and continuity?

__Intermediate Value Theorem for Derivatives__

- What is the Intermediate Value Theorem for Derivatives?

**STEP 3: Reading**

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