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

Sketch the graph of a function that satisfies all…

02:56

Question

Answered step-by-step

Problem 26 Easy Difficulty

Sketch the graph of a function that satisfies all of the given conditions

Vertical asymptote $ x = 0 $, $ f'(x) > 0 $ if $ x < -2 $,
$ f'(x) < 0 $ if $ x > -2 (x \not= 0) $,
$ f"(x) < 0 $ if $ x < 0 $, $ f"(x) > 0 $ if $ x > 0 $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Kian Manafi
Numerade Educator

Like

Report

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

More Answers

03:01

Fahad Paryani

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
Catherine Ross

Missouri State University

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

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

01:53

Sketch the graph of a func…

01:04

Sketch the graph of a func…

02:05

Sketch the graph of a func…

02:44

Sketch a graph of a functi…

00:35

Sketch the graph of the fu…

01:30

Sketch the graph of the fu…

01:53

Sketch the graph of the fu…

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 given four conditions that are graph has to meet you have this vertical ascent owed at X is equal to zero. We are increasing or are derivative is greater than zero when X is less than negative two were decreasing when X is greater than negative two. And our second derivative is less than zero for X being less than zero. And our second derivative being less than zero means that we are just concave down on the interval from negative infinity to zero. And so what I've drawn already is just the vertical ascent to X is equal to zero. And I put on the X axis this point negative too. Since that's the point where we go from increasing to decreasing. So I'm just gonna put a point up here as the point that we go from increasing to decreasing, which means that it is a local maximum. Or it could be an absolute maximum as well, but we're guaranteed to have a maximum at this point since we're going from increasing and decreasing. And so I'm going to draw a line that is concave down and increasing up until this point here just call that the point and now we're decreasing. Still concave down and we have this vertical ascent tote so we're never going to go past X is equal to zero. And now what we can do is we can actually just stop there since we don't have any conditions for X being greater than zero. So the important thing to remember is that we're decreasing until X is equal to negative two. And then we are sorry, we're increasing until X is equal to negative two. And then we start decreasing. And since we have this vertical ascent, oh, we're never going to go past zero. And we have to be always concave down which we are Yeah.

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
151
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
68
Hosted by: Alonso M
See More

Related Topics

Derivatives

Differentiation

Volume

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

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

01:53

Sketch the graph of a function that satisfies all of the given conditions. Ver…

01:04

Sketch the graph of a function that satisfies all of the given conditions. $$\b…

02:05

Sketch the graph of a function that satisfies all of the given conditions $ …

02:44

Sketch a graph of a function $f$ that has the given properties. $$ \begin{array…

00:35

Sketch the graph of the function, showing all asymptotes. $$f(x)=\frac{x}{1+x^{…

01:30

Sketch the graph of the function, showing all asymptotes. $$f(x)=\frac{x+1}{x-2…

01:53

Sketch the graph of the function, showing all asymptotes. $$f(x)=\frac{1}{(x+1)…
Additional Mathematics Questions

01:31

If a motor pump lifts 2,000 litres of water in 8 minutes, how many will it l…

01:29

Find the square root of 1536 by long division method ?

01:28

Rama planted a total 544 plants in 17 rows. How many plants did she put in e…

01:25

A stationary shop markdown their writing boards by 40%. The markdown is $32.…

02:50

What is the original price of an item that is being charged a tax of 20%, an…

01:30

Write a word problem that must be solved with division and includes 2/7 as t…

01:42

In a city, out of every 15 people, 1 person is a government servant. If 1354…

06:56

96 men were engaged for a project of constructing a railway track of the len…

01:41

after purchasing two copies of the same book,x sold the respectively at 0.8 …

03:10

A sum of Rs 30000 invested in a scheme where the interest gets compounded an…

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