## Section 5.4 - Modeling and Optimization

**Essential Question(s):**

Explain how derivatives, critical values, and extrema are used when optimizating situations.

**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.

__A Strategy for Optimization__

- What is a strategy for Solving Max-Min Problems? (pg 224)

__Examples from Mathematics__

- What are some optimization problems from mathematics? (Ex 1 & 2 pg 224 - 225)

__Examples from Business and Industry - OPTIONAL__

- What are some optimization problems from Business and Industry? (Ex 3 & 4 pg 226 - 227)

__Examples from Economics - OPTIONAL__

- What is maximum profit? (pg 228)
- How do you maximize profit? (Ex 5 pg 228)
- What is minimizing average cost? (pg 229)
- How do you minimize average cost? (Ex 6 pg 229 -230)

__Modeling Discrete Phenomena with Differentiable Functions - OPTIONAL__

- How is it possible to use functions with real number domains when the context of the problem requires integer values?

**STEP 3: Reading**

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

- Read pages 224 - 230.
- Make sure to read the paragraphs between the examples and sidebar snippets.