PreCalculus
Chapter 11 Trigonometric Derivatives
Unit 11-1 Zeros, Vertical Asymptotes, and POEs
- Standard 7a: Find Zeros, Vertical Asymptotes, and Points of Exclusion of a Rational Function and distinguish them from one another
Agenda
- Three Unique Points in a Rational Function
- Zeros - where only the numerator is zero
- Vertical Asymptotes (VA) - where only the denominator is zero
- Points of Exclusion (POE) - where both are zero
- Assignment 7-1: Pg 360 #1-5, 8, 11
Unit 11-2 Sign Patterns of Rational Functions
- Standard 7b: Determine the end behavior of a rational function from a model, polynomial long division, or infinite limits and sketch the horizontal or slant asymptote.
Agenda
- Limits as x approaches ±∞
- Asymptotes
- Horizontal at 0
- Horizontal at a line other than 0
- Slant Asymptotes
- Assignment 7-2:
Pg 373 #1-4, 7-14, 16-22
Unit 11-3 End Behavior: Horizontal Asymptotes
- Standard 7c: Find the derivative of a rational function using the Quotient Rule
- Standard 7d: Apply sign patterns to the first derivative.
- Standard 7e: Find the extreme points of a rational function
Agenda
- The Quotient Rule
- Sign Patterns of Rational Function Derivatives
- Finding Critical Points and Extreme Values Using the Quotient Rule
- Assignment 7-3: Part A Pg 382 #1-6 Part B Pg. 382 #10-11, 13, 14, 16, & 18
- Screencast
- Powerpoint
- PDF Slides
Unit 11-4 End Behavior: Slant Asymptotes
- Standard 7f: Use sign patterns to solve rational inequalities.
Agenda
- Review of Sign Patterns
- Denoting zeros, POE's, and vertical asymptotes on a number line
- Applying Sign Patterns to Rational Function Graphs
- Assignment 7-4: Part A Pg 390 #1-5 Part B #6-10
Unit 11-5 The Quotient Rule
- Standard 7c: Find the derivative of a rational function using the Quotient Rule
- Standard 7d: Apply sign patterns to the first derivative.
- Standard 7e: Find the extreme points of a rational function
Agenda
- The Quotient Rule
- Sign Patterns of Rational Function Derivatives
- Finding Critical Points and Extreme Values Using the Quotient Rule
- Assignment 7-3: Part A Pg 382 #1-6 Part B Pg. 382 #10-11, 13, 14, 16, & 18