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…

02:33

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

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

03:05

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

Anna Marie Vagnozzi

Campbell University

Samuel Hannah

University of Nottingham

Joseph Lentino

Boston College

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

01:05

Suppose $f "$ is cont…

01:00

$$
\begin{array}{l}{\te…

01:40

Suppose $f^{\prime \prime}…

01:45

# 17) Suppose f" is c…

01:25

If $f$ is continuous on $(…

01:08

If $f$ is continuous on $(…

02:27

If $f$ is continuous on $(…

01:19

If $f$ is continuous on $(…

01:18

If $ f $ is continuous on …

01:04

If $\mathrm{f}$ is continu…

01:15

If $f$ is continuous on $(…

01:15

If $f$ is continuous on $(…

01:00

If a continuous, different…

01:49

If a continuous, different…

01:01

If a continuous, different…

00:57

If a continuous, different…

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

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.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
71
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
46
Hosted by: Alonso M
See More

Related Topics

Derivatives

Differentiation

Volume

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Samuel Hannah

University of Nottingham

Joseph Lentino

Boston College

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

01:05

Suppose $f "$ is continuous on $(-\infty, \infty).$ $$\begin{array}{l}{\text {…

01:00

$$ \begin{array}{l}{\text { Suppose } f^{\prime \prime} \text { is continuous …

01:40

Suppose $f^{\prime \prime}$ is continuous on $(-\infty, \infty)$ (a) If $f^{\p…

01:45

# 17) Suppose f" is continous on (~0,0). (a) If f' (2) = 0 and f"(2) = -5 what …

01:25

If $f$ is continuous on $(-\infty, \infty),$ what can you say about its graph?

01:08

If $f$ is continuous on $(-\infty, \infty),$ what can you say about its graph?

02:27

If $f$ is continuous on $(-\infty, \infty),$ what can you say about its graph?

01:19

If $f$ is continuous on $(-\infty, \infty),$ what can you say about its graph?

01:18

If $ f $ is continuous on $ (-\infty, \infty) $, what can you say about its gra…

01:04

If $\mathrm{f}$ is continuous on $(-\infty, \infty),$ what can you say about it…

01:15

If $f$ is continuous on $(-\infty, \infty),$ what can you say about its graph?

01:15

If $f$ is continuous on $(-\infty, \infty),$ what can you say about its graph?

01:00

If a continuous, differentiable function $f$ is equal to 2 at $x=3$ and at $x=5…

01:49

If a continuous, differentiable function $f$ is equal to 2 at $x=3$ and at $x=5…

01:01

If a continuous, differentiable function $f$ has values $f(-2)=3$ and $f(4)=1$,…

00:57

If a continuous, differentiable function $f$ has values $f(-2)=3$ and $f(4)=1$,…
Additional Mathematics Questions

13:16

point)
Let f(x) = er How large should be so that the Midpoint Rule approx…

03:10

1. (5 points) Fill in the blanks NELCHANGE THEQREM: The integral of a
is …

01:37

An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of &quo…

03:23

point) Match the points labeled on the curve below with the given slopes in …

05:09

NCS
How many attended only the FSU- Butler game?
How many did not atte…

01:44

Required information Find counterexample; to the given universally quantifie…

01:25

The latest Canadian census asked every household for the age of each person …

03:38

The Elo Chess Rating System
method for predicting scores From
chess ma…

03:12

A recent nationa) survey found that high schoo students watched an average (…

02:51

Ihere is norelationship between the use Of social media andthe attention spa…

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
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started