INVERSE FUNCTIONS Section 5 3 Calculus APDual Revised

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INVERSE FUNCTIONS Section 5. 3 Calculus AP/Dual, Revised © 2017 viet. dang@humbleisd. net 3/5/2021

INVERSE FUNCTIONS Section 5. 3 Calculus AP/Dual, Revised © 2017 viet. dang@humbleisd. net 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 1

REVIEW 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 2

REVIEW 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 2

REVIEW EXAMPLE 1 {( 0, – 3), ( 2 , 1 ), ( 6

REVIEW EXAMPLE 1 {( 0, – 3), ( 2 , 1 ), ( 6 , 3 )} 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 3

REVIEW EXAMPLE 1 inverse 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse

REVIEW EXAMPLE 1 inverse 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 4

QUESTION If a function is a relation, is an inverse a function as well?

QUESTION If a function is a relation, is an inverse a function as well? inverse 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 5

REVIEW EXAMPLE 2 y = 3 x – 2 y = 3 x– 2

REVIEW EXAMPLE 2 y = 3 x – 2 y = 3 x– 2 x = 3 y – 2 x + 2 = 3 y 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 6

REVIEW 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 7

REVIEW 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 7

FURTHER EXPLANATION OF INVERSES 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse

FURTHER EXPLANATION OF INVERSES 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 8

REVIEW EXAMPLE 3 Is this graph a function? Does it have an inverse? Is

REVIEW EXAMPLE 3 Is this graph a function? Does it have an inverse? Is it one–to–one function and monotonic? 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 9

REVIEW EXAMPLE 4 Is this graph a function? Does it have an inverse? Is

REVIEW EXAMPLE 4 Is this graph a function? Does it have an inverse? Is it one–to–one function and monotonic? 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 10

REVIEW EXAMPLE 5 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions

REVIEW EXAMPLE 5 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 11

THE DERIVATIVE OF AN INVERSE FUNCTION 3/5/2021 7: 33 AM § 5. 3: Derivative

THE DERIVATIVE OF AN INVERSE FUNCTION 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 12

STEPS 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 13

STEPS 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 13

THE DERIVATIVE OF THE INVERSE 3/5/2021 7: 33 AM § 5. 3: Derivative of

THE DERIVATIVE OF THE INVERSE 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 14

THE DERIVATIVE OF THE INVERSE 3/5/2021 7: 33 AM § 5. 3: Derivative of

THE DERIVATIVE OF THE INVERSE 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 15

PROVING THE INVERSE POINT’S SLOPE 3/5/2021 7: 33 AM § 5. 3: Derivative of

PROVING THE INVERSE POINT’S SLOPE 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions Point Slope 16

EXAMPLE 1 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 17

EXAMPLE 1 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 17

EXAMPLE 1 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 18

EXAMPLE 1 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 18

EXAMPLE 1 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 19

EXAMPLE 1 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 19

EXAMPLE 2 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 20

EXAMPLE 2 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 20

EXAMPLE 2 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 21

EXAMPLE 2 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 21

EXAMPLE 3 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 22

EXAMPLE 3 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 22

YOUR TURN 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 23

YOUR TURN 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 23

EXAMPLE 4 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 24

EXAMPLE 4 3/5/2021 7: 33 AM § 5. 3: Derivative of Inverse Functions 24

YOUR TURN 3/5/2021 7: 34 AM § 5. 3: Derivative of Inverse Functions 25

YOUR TURN 3/5/2021 7: 34 AM § 5. 3: Derivative of Inverse Functions 25

EXAMPLE 5 3/5/2021 7: 34 AM § 5. 3: Derivative of Inverse Functions 26

EXAMPLE 5 3/5/2021 7: 34 AM § 5. 3: Derivative of Inverse Functions 26

EXAMPLE 6 3/5/2021 7: 34 AM § 5. 3: Derivative of Inverse Functions 27

EXAMPLE 6 3/5/2021 7: 34 AM § 5. 3: Derivative of Inverse Functions 27

YOUR TURN 3/5/2021 7: 34 AM § 5. 3: Derivative of Inverse Functions 28

YOUR TURN 3/5/2021 7: 34 AM § 5. 3: Derivative of Inverse Functions 28

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) 3/5/2021 7: 34 AM § 5. 3:

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) 3/5/2021 7: 34 AM § 5. 3: Derivative of Inverse Functions 29

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) Vocabulary 3/5/2021 7: 34 AM Process and

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) Vocabulary 3/5/2021 7: 34 AM Process and Connections § 5. 3: Derivative of Inverse Functions Answer and Justifications 30

ASSIGNMENT Worksheet 3/5/2021 7: 34 AM § 5. 3: Derivative of Inverse Functions 31

ASSIGNMENT Worksheet 3/5/2021 7: 34 AM § 5. 3: Derivative of Inverse Functions 31