Problem

Sketch the graph of a function that satisfies all…

02:33

Question

Answered step-by-step

Problem 23 Easy Difficulty

Suppose $ f" $ is continuous on $ (-\infty, \infty) $.
(a) If $ f'(2) = 0 $ and $ f"(2) = -5 $, what can you say about $ f $?
(b) If $ f'(6) = 0 $ and $ f"(6) = 0 $, what can you say about $ f $?

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Kian Manafi

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Watch More Solved Questions in Chapter 4

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

Problem 87

Problem 88

Problem 89

Problem 90

Problem 91

Problem 92

Problem 93

Video Transcript

this funk are in this problem that are second derivative F double prime of X is continuous for all real numbers or from negative infinity to infinity. And in part they were told that F prime of two is equal to zero, n. f double prime of two is equal to negative five. And were asked, what can we say about this function given this information? Well, since we know that F prime of two is equal to zero, that means that we have a critical point At X is equal to two, which means that X is equal to two. We could have a local maximum or minimum value. And since we know the sign of our second derivative at this point X is equal to two, we can tell whether this is a maximum or minimum. Since this sign of our second derivative at X is equal to two is negative. So since second derivative at X equal to two is less than zero. That means that this is a local maximum. So we know that we have a local maximum and this is from the second derivative test At X is equal to two. If the second derivative was greater than zero, then it would have been a local minimum. So what we can tell from F prime of two being equal to zero and F double prime of two being equal to negative five is that we have a local maximum at X is equal to two. And now for part B we're told that F prime of X or F prime of six is equal to zero and F double prime of X. Sorry, for double prime of six Is also equal to zero. So we know that there is a critical point, Since our derivative is equal to zero At this point X is equal to six. So critical point, uh X is equal to six. And since our second derivative at X or at six is equal to zero, um That means that this isn't a local maximum or a local minimum for it to be a local maximum minimum, this double prime of six would have had to been positive or negative. But since it's equal to zero, that means at this point At f double prime of X or f double prime of six could be an inflection point. So potential inflection point at X is equal to six, but it is not a local maximum minimum, since our second derivative isn't positive or negative.

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem

Sketch the graph of a function that satisfies all…

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 2 / BC Educators

Catherine Ross

Anna Marie Vagnozzi

Samuel Hannah

Joseph Lentino

Calculus 2 / BC Courses

Recommended Videos

Watch More Solved Questions in Chapter 4

Video Transcript

James Stewart

Calculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Samuel Hannah

Joseph Lentino

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Samuel Hannah

Joseph Lentino

James StewartCalculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Samuel Hannah

Joseph Lentino

James Stewart

Calculus: Early Transcendentals