Problem

Estimate the intervals of concavity to one decima…

01:53

Question

Answered step-by-step

Problem 62 Hard Difficulty

(a) Use a graph of $ f $ to give a rough estimate of the intervals of concavity and the coordinates of the points of inflection.
(b) use a graph of $ f" $ to give better estimates.

$ f(x) = (x - 1)^2 (x + 1)^3 $

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Fahad Paryani

Numerade Educator

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

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

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

Okay, so we're being asked to use the graph of F Forgive a rough estimate of thie interrupt, contact bree in accordance appointed inflection. So let's go ahead and start. And so contact when it is cranking up when it has that sort of u shape to the function in this case, dislike hers. You could see this u shaped right here on occurred from negative one to some number right here. We can say negative zero point two. This is only a rough estimate, and they're gonna want to negative zero point two approximately. And then we see it again somewhere over here, but a little bit closer to one. So this is going to be something like point seven. So you see this kind of shape, but it goes forever. So will be one seven to infinity and then concave down the upside down u shape. You could see that between you could see that between negative zero point two and point seven, and we can also see it right here. This's a little bit harder to tell that this is a upside down you shape. So from negative infinity to negative one so negative and serenity, negative one. So that means the points of inflection occurs when the sign children does the crews. That negative one. Um negative. Teo point two. And at zero point seven. And those are rough estimates. And to find we're going to be using a graph of double prime to get us a better estimate. Ah, so we take the graph of F double prime and after we'LL try back to his vehicle. Ah, if you take the derivative again, you get twenty x cube, close twelve X squared, minus twelve X minus four. And we're looking for when this is equal to zero. So to give us a better estimate of how where the con cavities are and I took delivery of drawing out thes of function And as you can see, our approximation wasn't that bad. We had negative one zero, and then it is at negative. They're going to nine. Very good. And in point six nine. So we didn't have that bad of an approximation, so I could have, and that's Ah, this is when it crosses. So this is going from negative to positive. So this is negative. His Khan came down the continent down from negative infinity to negative one, just in case you did not read it. And if it's positive this conclave up, so anything above anything after negative one zero and it changes again. And negative zero point two nine, which we estimated again, disaster closure, important threes. But we have Point Teo that bad either. And then it changes again. At point six nine, we said point seven, which isn't as horrible as well in our inflection points are also correct, so that is it.

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

Estimate the intervals of concavity to one decima…

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

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 2 / BC Educators

Grace He

Catherine Ross

Kristen Karbon

Samuel Hannah

Calculus 2 / BC Courses

Recommended Videos

Watch More Solved Questions in Chapter 4

Video Transcript

James Stewart

Calculus: Early Transcendentals

Grace He

Catherine Ross

Kristen Karbon

Samuel Hannah

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

Calculus: Early Transcendentals

Grace He

Catherine Ross

Kristen Karbon

Samuel Hannah

James StewartCalculus: Early Transcendentals

Grace He

Catherine Ross

Kristen Karbon

Samuel Hannah

James Stewart

Calculus: Early Transcendentals