Problem

Where is the function $ h(x) = \mid x - 1 \mid + …

02:50

Problem 73 Hard Difficulty

(a) For what values of $ x $ is the function $ f(x) = \mid x^2 - 9 \mid $ differentiable? Find a formula for $ f'. $
(b) Sketch the graph of $ f $ and $ f'. $

Answer

(a) $f$ is not differentiable at 3 or at -3
(B)

More Answers

00:40

Frank L.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Discussion

You must be signed in to discuss.

Top Calculus 1 / AB Educators

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Joseph L.

Boston College

Watch More Solved Questions in Chapter 3

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Problem 81

Problem 82

Problem 83

Problem 84

Problem 85

Problem 86

Video Transcript

you know, it's clear a seven inning right here. So we have X squared minus nine. The absolute value we're first going to calculate. We're making a equal to zero. Let me get access equal to positive or negative three. So f of X is not different. Shovel there. We know that Y is equal to X square minus nine. This is gonna be an upward open opening parabola aboard opening crapola and have Ciro's a positive and negative three. So when access less than or equal to negative three and when access bigger or equal to three you have f of X is equal to X square minus nine. We don't need the absolute value signs, since it's already gonna be positive. And when access between negative three and three we get half of X is equal to negative X Square minus nine, which gives us negative X Square plus nine. So when we differentiate for the first part, we get the derivative where X Square minus nine is equal to two x and for access between negative three and three. This is negative. X Square plus nine. We get negative to USC's. So we our answer is it is not different. Chewable at X is equal to positive or negative free and are derivative. Is equal to two X If X is less than negative. Three or ex this bigger than three. Negative to X for access between negative three and positive three. Next, we're going to grab this. So if we grab our original well, look like this then are derivative says that six negative six.

Clarissa N.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Top Calculus 1 / AB Educators

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Joseph L.

Boston College