SLOPE FIELDS Section 6 1 Calculus APDual Revised

SLOPE FIELDS Section 6. 1 Calculus AP/Dual, Revised © 2018 viet. dang@humbleisd. net 1/2/2022 9: 19 PM § 6. 1: Slope Fields 1

TWO TECHNIQUES FOR APPROXIMATING SOLUTIONS OF DIFFERENTIAL EQUATIONS 1/2/2022 9: 19 PM § 6. 1: Slope Fields 2

SLOPE FIELDS A. A graphical approach to solving a differential equation is called a slope field B. The slope, or direction, at each point of a differential equation: Horizontally, Vertically, and Diagonally C. Vector fields have direction whereas Slope fields do not 1/2/2022 9: 20 PM § 6. 1: Slope Fields 3

REAL-LIFE EXAMPLES 1/2/2022 9: 20 PM § 6. 1: Slope Fields 4

STEPS 1/2/2022 9: 20 PM § 6. 1: Slope Fields 5

REVIEW 1/2/2022 9: 20 PM § 6. 1: Slope Fields 6

CREATING THE SLOPE FIELD 1/2/2022 9: 20 PM § 6. 1: Slope Fields 7

EXAMPLE 1 1/2/2022 9: 20 PM § 6. 1: Slope Fields 8

EXAMPLE 2 1/2/2022 9: 20 PM § 6. 1: Slope Fields 9

EXAMPLE 3 1/2/2022 9: 20 PM § 6. 1: Slope Fields 10

YOUR TURN 1/2/2022 9: 20 PM § 6. 1: Slope Fields 11

EXAMPLE 4 1/2/2022 9: 20 PM § 6. 1: Slope Fields 12

EXAMPLE 5 1/2/2022 9: 20 PM § 6. 1: Slope Fields 13

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) 1/2/2022 9: 21 PM § 6. 1: Slope Fields 14

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) The slope field for a certain differential equation is shown below. Which of the following could be a specific solution to the differential equation? Vocabulary 1/2/2022 9: 21 PM Connections and Process § 6. 1: Slope Fields Answer and Justifications 15

ASSIGNMENT Worksheet 1/2/2022 9: 21 PM § 6. 1: Slope Fields 16