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
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