CONCAVITY Section 3 4 Calculus APDual Revised 2017

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CONCAVITY Section 3. 4 Calculus AP/Dual, Revised © 2017 viet. dang@humbleisd. net 10/26/2021 11:

CONCAVITY Section 3. 4 Calculus AP/Dual, Revised © 2017 viet. dang@humbleisd. net 10/26/2021 11: 59 AM § 3. 4: Concavity 1

REVIEW EXAMPLE 10/26/2021 11: 59 AM § 3. 4: Concavity 2

REVIEW EXAMPLE 10/26/2021 11: 59 AM § 3. 4: Concavity 2

REVIEW EXAMPLE 10/26/2021 11: 59 AM § 3. 4: Concavity 3

REVIEW EXAMPLE 10/26/2021 11: 59 AM § 3. 4: Concavity 3

F’ VS F’’ 1) INCREASING OR DECREASING BASED 1) ON SLOPE 2) RELATIVE MINIMUM

F’ VS F’’ 1) INCREASING OR DECREASING BASED 1) ON SLOPE 2) RELATIVE MINIMUM OR MAXIMUM 10/26/2021 11: 59 AM § 3. 4: Concavity CONCAVITY POINT OF INFLECTION 4

CONCAVITY 10/26/2021 11: 59 AM § 3. 4: Concavity 5

CONCAVITY 10/26/2021 11: 59 AM § 3. 4: Concavity 5

FIRST DERIVATIVE GRAPHS 10/26/2021 11: 59 AM § 3. 4: Concavity 6

FIRST DERIVATIVE GRAPHS 10/26/2021 11: 59 AM § 3. 4: Concavity 6

FIRST DERIVATIVE GRAPHS 10/26/2021 12: 00 PM § 3. 4: Concavity 7

FIRST DERIVATIVE GRAPHS 10/26/2021 12: 00 PM § 3. 4: Concavity 7

CONCAVITY – – + + 10/26/2021 12: 00 PM § 3. 4: Concavity 8

CONCAVITY – – + + 10/26/2021 12: 00 PM § 3. 4: Concavity 8

CONCAVE UP OR CONCAVE DOWN 10/26/2021 12: 00 PM § 3. 4: Concavity 9

CONCAVE UP OR CONCAVE DOWN 10/26/2021 12: 00 PM § 3. 4: Concavity 9

REVIEW EXAMPLE 10/26/2021 12: 00 PM § 3. 4: Concavity 10

REVIEW EXAMPLE 10/26/2021 12: 00 PM § 3. 4: Concavity 10

TO DETERMINE CONCAVITY 10/26/2021 12: 00 PM § 3. 4: Concavity 11

TO DETERMINE CONCAVITY 10/26/2021 12: 00 PM § 3. 4: Concavity 11

EXAMPLE 1 10/26/2021 12: 00 PM § 3. 4: Concavity 12

EXAMPLE 1 10/26/2021 12: 00 PM § 3. 4: Concavity 12

EXAMPLE 1 10/26/2021 12: 00 PM § 3. 4: Concavity 13

EXAMPLE 1 10/26/2021 12: 00 PM § 3. 4: Concavity 13

EXAMPLE 1 10/26/2021 12: 00 PM § 3. 4: Concavity 14

EXAMPLE 1 10/26/2021 12: 00 PM § 3. 4: Concavity 14

EXAMPLE 2 10/26/2021 12: 00 PM § 3. 4: Concavity 15

EXAMPLE 2 10/26/2021 12: 00 PM § 3. 4: Concavity 15

YOUR TURN 10/26/2021 12: 00 PM § 3. 4: Concavity 16

YOUR TURN 10/26/2021 12: 00 PM § 3. 4: Concavity 16

EXAMPLE 3 10/26/2021 12: 00 PM § 3. 4: Concavity 17

EXAMPLE 3 10/26/2021 12: 00 PM § 3. 4: Concavity 17

EXAMPLE 3 (PRODUCT RULE) 10/26/2021 12: 00 PM § 3. 4: Concavity 18

EXAMPLE 3 (PRODUCT RULE) 10/26/2021 12: 00 PM § 3. 4: Concavity 18

EXAMPLE 3 (PRODUCT RULE) 10/26/2021 12: 00 PM § 3. 4: Concavity 19

EXAMPLE 3 (PRODUCT RULE) 10/26/2021 12: 00 PM § 3. 4: Concavity 19

EXAMPLE 3 (QUOTIENT RULE) 10/26/2021 12: 00 PM § 3. 4: Concavity 20

EXAMPLE 3 (QUOTIENT RULE) 10/26/2021 12: 00 PM § 3. 4: Concavity 20

EXAMPLE 3 (QUOTIENT RULE) 10/26/2021 12: 00 PM § 3. 4: Concavity 21

EXAMPLE 3 (QUOTIENT RULE) 10/26/2021 12: 00 PM § 3. 4: Concavity 21

EXAMPLE 3 10/26/2021 12: 00 PM § 3. 4: Concavity 22

EXAMPLE 3 10/26/2021 12: 00 PM § 3. 4: Concavity 22

EXAMPLE 3 10/26/2021 12: 00 PM § 3. 4: Concavity 23

EXAMPLE 3 10/26/2021 12: 00 PM § 3. 4: Concavity 23

EXAMPLE 4 10/26/2021 12: 00 PM § 3. 4: Concavity 24

EXAMPLE 4 10/26/2021 12: 00 PM § 3. 4: Concavity 24

EXAMPLE 4 10/26/2021 12: 00 PM § 3. 4: Concavity 25

EXAMPLE 4 10/26/2021 12: 00 PM § 3. 4: Concavity 25

EXAMPLE 4 10/26/2021 12: 00 PM § 3. 4: Concavity 26

EXAMPLE 4 10/26/2021 12: 00 PM § 3. 4: Concavity 26

EXAMPLE 4 10/26/2021 12: 00 PM § 3. 4: Concavity 27

EXAMPLE 4 10/26/2021 12: 00 PM § 3. 4: Concavity 27

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) 10/26/2021 12: 00 PM § 3. 4:

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) 10/26/2021 12: 00 PM § 3. 4: Concavity 28

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) Vocabulary 10/26/2021 12: 00 PM Connections and

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) Vocabulary 10/26/2021 12: 00 PM Connections and Process § 3. 4: Concavity Answer and Justifications 29

ASSIGNMENT Page 192 3 -25 odd & Justify 10/26/2021 12: 00 PM § 3.

ASSIGNMENT Page 192 3 -25 odd & Justify 10/26/2021 12: 00 PM § 3. 4: Concavity 30