INTERMEDIATE VALUE THEOREM Section 1 4 B Calculus

INTERMEDIATE VALUE THEOREM Section 1. 4 B Calculus AP/Dual, Revised © 2017 viet. dang@humbleisd. net 1/5/2022 2: 58 AM § 1. 4 B: Intermediate Value Theorem 1

DEFINITION OF CONTINUITY 1/5/2022 2: 58 AM § 1. 4 B: Intermediate Value Theorem 2

EXAMPLES OF DISCONTINUOUS 1/5/2022 2: 58 AM § 1. 4 B: Intermediate Value Theorem 3

PROOF OF INTERMEDIATE VALUE THEOREM Can you prove that at one time, you were exactly 5. 2578 feet tall? 1/5/2022 2: 58 AM § 1. 4 B: Intermediate Value Theorem 4

INTERMEDIATE VALUE THEOREM 1/5/2022 2: 58 AM § 1. 4 B: Intermediate Value Theorem 5

EXAMPLE 1 1/5/2022 2: 58 AM § 1. 4 B: Intermediate Value Theorem 6

EXAMPLE 2 1/5/2022 2: 58 AM § 1. 4 B: Intermediate Value Theorem 7

EXAMPLE 3 These are the two extremes. 1/5/2022 2: 59 AM § 1. 4 B: Intermediate Value Theorem 8

EXAMPLE 3 1/5/2022 2: 59 AM § 1. 4 B: Intermediate Value Theorem 9

EXAMPLE 4 1/5/2022 2: 59 AM § 1. 4 B: Intermediate Value Theorem 10

EXAMPLE 4 (EXTENSION) 1/5/2022 2: 59 AM § 1. 4 B: Intermediate Value Theorem 11

EXAMPLE 5 1/5/2022 2: 59 AM § 1. 4 B: Intermediate Value Theorem 12

YOUR TURN 1/5/2022 2: 59 AM § 1. 4 B: Intermediate Value Theorem 13

TO EARN FULL CREDIT: 1/5/2022 2: 59 AM § 1. 4 B: Intermediate Value Theorem 14

PIECEWISE FUNCTIONS A. For a piecewise function to be continuous each function must be continuous on its specified interval and the limit of the endpoints of each interval must be equal. 1/5/2022 2: 59 AM § 1. 4 B: Intermediate Value Theorem 15

EXAMPLE 6 1/5/2022 2: 59 AM § 1. 4 B: Intermediate Value Theorem 16

EXAMPLE 6 1/5/2022 2: 59 AM § 1. 4 B: Intermediate Value Theorem 17

EXAMPLE 6 1/5/2022 2: 59 AM § 1. 4 B: Intermediate Value Theorem 18

IN CONCLUSION… A function exists when: 1. Point Exists 2. Limit Exists 3. Limit = Point 1/5/2022 2: 59 AM § 1. 4 B: Intermediate Value Theorem 19

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) 1/5/2022 2: 59 AM § 1. 4 B: Intermediate Value Theorem 20

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) Vocabulary 1/5/2022 2: 59 AM Connections and Process § 1. 4 B: Intermediate Value Theorem Answer and Justifications 21

ASSIGNMENT Worksheet 1/5/2022 2: 59 AM § 1. 4 B: Intermediate Value Theorem 22