Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Use the methods of this section to sketch the cur…

00:34

Question

Answered step-by-step

Problem 57 Medium Difficulty

Suppose the derivative of a function $ f $ is $ f'(x) = (x + 1)^2 (x - 3)^5 (x - 6)^4 $. On what interval is $ f $ increasing?


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Fahad Paryani
Numerade Educator

Like

Report

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

Related Topics

Derivatives

Differentiation

Volume

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Grace He
Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Caleb Elmore

Baylor University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

Video Thumbnail

06:14

Review

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

Join Course
Recommended Videos

02:19

Suppose the derivative of …

02:27

Suppose the derivative of …

0:00

Suppose the derivative of …

02:24

On what interval is the fu…

01:05

On what interval is the fu…

02:00

On what interval is the fu…

01:25

On what interval is the fu…

01:45

a) find the derivative, $f…

03:23

Determine the interval(s) …

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 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
Problem 93

Video Transcript

Okay, so we're told that the derivative FSF private bank and it's written right here and we're being ass on one into was f increase. So what we are going to do is we're going to look at So this does many different ways to do this. For some, it may be obvious for some, not B. I'm going to try to make it as obvious as possible. So we see that we have, ah, square A to the fifth and to the fourth. And so we know that any number squared were always deposited in any number two. The fourth will always also deposited. But this will not always be positive, so we can do this. Fifteen tells us that is being a small flying ex ministry five times X minus three times X minus three times minus three times X minus two times expensive. So what? I'm going to do it. I'm gonna pull one of those x minus three out and it's going to give us prime of eggs equals X plus one. So these are going to remain the same. That was one squared times X minus three to the forint. Times X minus six. Tune in for it times X minus two And so now it should be a little bit more clear. All the least three terms are always positive, so they're going to be always greater than do that. They're always going to be a greater than Teo positive. And so that means the sign of the function of prime is determined by this guy. Wrote your ex ministry. So when three minutes when X is greater than three, that is only appointed in which justice term right here is positive. So that means the sign Ah, whenever the sign of f promise positive. That's when efforts increasing, so it is increasing from three to infinity.

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.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
175
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
75
Hosted by: Alonso M
See More

Related Topics

Derivatives

Differentiation

Volume

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Caleb Elmore

Baylor University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

Video Thumbnail

06:14

Review

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

Join Course
Recommended Videos

02:19

Suppose the derivative of a function $f$ is $f^{\prime}(x)=(x+1)^{2}(x-3)^{5}(x…

02:27

Suppose the derivative of f is f ' ( x ) = ( x + 1 ) 4 ( x − 5 ) 5 ( x − 6 ) 6 …

0:00

Suppose the derivative of a function $f$ is $$ f^{\prime}(x)=(x-4)^{2}(x+3)^{7}…

02:24

On what interval is the function $f(x)=5 x-e^{x}$ increasing?

01:05

On what interval is the function $f(x)=x^{3} e^{x}$ increasing?

02:00

On what interval is the function $f(x)=e^{3 x}-e^{x}$ increasing?

01:25

On what interval is the function $f(x)=e^{3 x}-e^{x}$ increasing?

01:45

a) find the derivative, $f^{\prime}(x),$ b) indicate the interval(s) for which …

03:23

Determine the interval(s) on which the function is increasing and decreasing. …
Additional Mathematics Questions

03:41

13) The third term in a sequence is 36. The fifth term is 324. What are the …

03:06

Instructions: Write the point-slope form of each graph: Use the red point - …

02:40

Integers are made using some or all of the digits 1, 2, 3,4, 5 and 6 Each in…

02:03

12. Sketch triangle and label its vertices. Name two sides and the included …

03:09

Following is the probability distribution of a random variable that represen…

01:47

In a hypothesis test for the equality of two population means, the p-value i…

01:58

In 4 CDE, U is the centroid (point Of concurrency of the medians of the tria…

03:18

15. Determine how (if possible) the triangles can be proved similar:
24

01:04

2 Two sides of a triangle have the measures 35 and 12, Find the range of pos…

02:21

3 Given: AB BC, BC = BD Prove: B is the midpoint of line segment AD mD

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started