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 12/12/2021

INVERSE FUNCTIONS Section 5. 3 Calculus AP/Dual, Revised © 2017 viet. dang@humbleisd. net 12/12/2021 8: 42 AM § 5. 3: Derivative of Inverse Functions 1

REVIEW 12/12/2021 8: 42 AM § 5. 3: Derivative of Inverse Functions 2

REVIEW 12/12/2021 8: 42 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 )} 12/12/2021 8: 42 AM § 5. 3: Derivative of Inverse Functions 3

REVIEW EXAMPLE 1 inverse 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse

REVIEW EXAMPLE 1 inverse 12/12/2021 8: 43 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 12/12/2021 8: 43 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 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 6

REVIEW 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 7

REVIEW 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 7

FURTHER EXPLANATION OF INVERSES 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse

FURTHER EXPLANATION OF INVERSES 12/12/2021 8: 43 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? 12/12/2021 8: 43 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? 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 10

REVIEW EXAMPLE 5 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions

REVIEW EXAMPLE 5 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 11

THE DERIVATIVE OF AN INVERSE FUNCTION 12/12/2021 8: 43 AM § 5. 3: Derivative

THE DERIVATIVE OF AN INVERSE FUNCTION 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 12

STEPS 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 13

STEPS 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 13

THE DERIVATIVE OF THE INVERSE 12/12/2021 8: 43 AM § 5. 3: Derivative of

THE DERIVATIVE OF THE INVERSE 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 14

THE DERIVATIVE OF THE INVERSE 12/12/2021 8: 43 AM § 5. 3: Derivative of

THE DERIVATIVE OF THE INVERSE 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 15

PROVING THE INVERSE POINT’S SLOPE Point 12/12/2021 8: 43 AM § 5. 3: Derivative

PROVING THE INVERSE POINT’S SLOPE Point 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions Slope Point Slope 16

EXAMPLE 1 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 17

EXAMPLE 1 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 17

EXAMPLE 1 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 18

EXAMPLE 1 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 18

EXAMPLE 1 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 19

EXAMPLE 1 12/12/2021 8: 43 AM § 5. 3: Derivative of Inverse Functions 19

EXAMPLE 2 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 20

EXAMPLE 2 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 20

EXAMPLE 2 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 21

EXAMPLE 2 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 21

EXAMPLE 3 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 22

EXAMPLE 3 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 22

YOUR TURN 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 23

YOUR TURN 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 23

EXAMPLE 4 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 24

EXAMPLE 4 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 24

YOUR TURN 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 25

YOUR TURN 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 25

EXAMPLE 5 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 26

EXAMPLE 5 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 26

EXAMPLE 6 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 27

EXAMPLE 6 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 27

YOUR TURN 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 28

YOUR TURN 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 28

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) 12/12/2021 8: 44 AM § 5. 3:

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 29

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) Vocabulary 12/12/2021 8: 44 AM Process and

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) Vocabulary 12/12/2021 8: 44 AM Process and Connections § 5. 3: Derivative of Inverse Functions Answer and Justifications 30

ASSIGNMENT Worksheet 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 31

ASSIGNMENT Worksheet 12/12/2021 8: 44 AM § 5. 3: Derivative of Inverse Functions 31

INVERSE FUNCTIONS Section 5 3 Calculus APDual RevisedINVERSE FUNCTIONS Section 5 3 Calculus APDual Revised
7 INVERSE FUNCTIONS INVERSE FUNCTIONS 7 6 Inverse7 INVERSE FUNCTIONS INVERSE FUNCTIONS 7 6 Inverse
7 INVERSE FUNCTIONS INVERSE FUNCTIONS 7 6 Inverse7 INVERSE FUNCTIONS INVERSE FUNCTIONS 7 6 Inverse
7 INVERSE FUNCTIONS INVERSE FUNCTIONS 7 6 Inverse7 INVERSE FUNCTIONS INVERSE FUNCTIONS 7 6 Inverse
POLAR COORDINATES Section 11 5 Calculus APDual RevisedPOLAR COORDINATES Section 11 5 Calculus APDual Revised
RELATED RATES Section 2 6 Calculus APDual RevisedRELATED RATES Section 2 6 Calculus APDual Revised
OPTIMIZATION Section 3 7 A Calculus APDual RevisedOPTIMIZATION Section 3 7 A Calculus APDual Revised
PARTICLE MOTION Section 3 7 Calculus APDual RevisedPARTICLE MOTION Section 3 7 Calculus APDual Revised
CONCAVITY Section 3 4 Calculus APDual Revised 2017CONCAVITY Section 3 4 Calculus APDual Revised 2017
RIEMANNS SUM Section 4 2 Calculus APDual RevisedRIEMANNS SUM Section 4 2 Calculus APDual Revised
MOTION Section 7 5 A Calculus APDual RevisedMOTION Section 7 5 A Calculus APDual Revised
SLOPE FIELDS Section 6 1 Calculus APDual RevisedSLOPE FIELDS Section 6 1 Calculus APDual Revised
USUBSTITUTION Section 4 5 Calculus BC APDual RevisedUSUBSTITUTION Section 4 5 Calculus BC APDual Revised
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