Problem

If $ a $ and $ b $ are positive numbers, prove th…

03:55

Question

Answered step-by-step

Problem 69 Medium Difficulty

Is there a number that is exactly 1 more than its cube?

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Daniel Jaimes

Numerade Educator

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

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 5

Continuity

Discussion

You must be signed in to discuss.

Top Calculus 1 / AB Educators

Watch More Solved Questions in Chapter 2

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

Video Transcript

This is problem number sixty nine of this tour Calculus, eighth edition, section two point five. Their number. That is exactly one more than its cube. Another way of saying this. If we take the number two b x can one number equal can one number acts equal one more, then that name that number. Cute. So this is what the equation is that we're trying to solve for. And if we rearrange this equation setting equal to zero, we can treat this as finding the route of the function where F is equal to execute, plus one minus X. And we wantto prove that there is a route to this function because then that would prove that there is a solution to the question given. And we're going to use the intermediate value through to confirm that. And with a lot of trial in there, we can choose a certain into role. In this case, we're going to choose an general from negative to to To where at negative, too. The function evaluated at native to gives. Thank you, Terry. Plus three, which is negative. Five and and two. We get eight plus one minus two or seven. So What we see here is that in the interval, from negative to to to the function takes on all the values from negative five to seven. For the reason that the function f is continuous, we see that this function is a polynomial which is always continuous. Ah, for the domain of all real numbers and in the specific interval from negative to to to thing values, much must range between this negative five and the seven. And since eagles from negative too positive, it must take the value zero, which is what we are interested in. We have confirmed in this interval specifically, there exists a number. According to the interment media Valley theme, there exist a number. There exists an X value that makes the statement true that we can figure out index value for which the function F is equal to zero. So we have confirmed that there does indeed exist a number that is exactly one more and it's cute According to the intermediate value, Theo

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

If $ a $ and $ b $ are positive numbers, prove th…

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

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 1 / AB Educators

Grace He

Anna Marie Vagnozzi

Caleb Elmore

Michael Jacobsen

Calculus 1 / AB Courses

Recommended Videos

Watch More Solved Questions in Chapter 2

Video Transcript

James Stewart

Calculus: Early Transcendentals

Grace He

Anna Marie Vagnozzi

Caleb Elmore

Michael Jacobsen

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

Calculus: Early Transcendentals

Grace He

Anna Marie Vagnozzi

Caleb Elmore

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Grace He

Anna Marie Vagnozzi

Caleb Elmore

Michael Jacobsen

James Stewart

Calculus: Early Transcendentals