PreCalculus
Chapter 6
Unit 6-1 Critical Values and Extreme Points of a Polynomial Function
- Standard 6a: Use the derivative to find the critical values of a polynomial
- Standard 6b: Use sign patterns to determine the intervals where a function is increasing or decreasing
Outline
- Using the Derivative to find Critical Points
- When the derivative is 0
- Interpreting the sign patterns of the derivative
- When is a function increasing/decreasing?
- Extreme Values
- Using the Extreme Values to find the Range of a Polynomial
- Assignment 6-1: Part A Pg 352 #1-11 Part B #12-14
Unit 6-2 Interpreting the Sign Pattern of the First Derivative
- Standard 6c: Identify the type of extreme point represented by a particular critical value
Outline
- Use Sign Patterns to Distinguish Minima from Maxima
- Absolute versus Relative Extreme Points
- Using the y value to distinguish Absolute from Relative Extremes
- Check the Endpoints in a Restricted Domain
- Assignment 6-2: Part A Pg 363 #11-18, 20 Part B Pg 362 #1-6, 23, 24
Unit 6-3 Optimization Problems
- Standard 6d: Use the derivative to solve optimization problems
Outline
- Review of Optimization with the Calculator (Std 1g)
- Optimization using the Derivative
- Setting up the function for the value to be optimized
- Using the Derivative to find the critical values
- Three Typical Examples of Optimization with Derivatives
- Assignment 6-3: Pg 375 #2-10
Unit 6-4 General Polynomial Sketching
- Standard 6e: Sketch a polynomial graph using the traits of Domain, x and y intercepts, End Behavior, Extreme Points, and Range
Outline
- Traits of a Polynomial Function
- Domain
- y-intercept
- Zeros
- End Behavior
- Extreme Points
- Range
- Using the Graphing Calculator to Verify Traits
- Assignment 6-4: Pg 388 #1, 5, 6, 9, 10, 11, 13, 14