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

(a) Find the intervals of increase or decrease. …

04:15

Question

Answered step-by-step

Problem 42 Hard Difficulty

(a) Find the intervals of increase or decrease.
(b) Find the local maximum and minimum values.
(c) Find the intervals of concavity and the inflection points.
(d) Use the information from parts $ (a) - (c) $ to sketch the graph.
Check your work with a graphing device if you have one.

$ h(x) = 5x^3 - 3x^5 $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Clarissa Noh
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Clarissa Noh

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
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

04:36

(a) Find the intervals of …

0:00


(a) Find the intervals…

05:23

(a) Find the intervals of …

02:09

(a) Find the intervals of …

01:47

(a) Find the intervals of …

0:00


(a) Find the intervals…

04:02

(a) Find the intervals of …

03:14

(a) Find the intervals of …

05:23

(a) Find the intervals of …

05:23

(a) Find the intervals of …

0:00


(a) Find the intervals…

02:43

(a) Find the intervals of …

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

he has close the would name right here. So we're gonna first find the derivative of H. We got 15 x square minus 15 X to the fourth. Then we take negative 15 up square. Get X minus one X plus one. So it's increasing. Negative one calm. A zero zero comma one and decreasing. Negative. Infinity. Negative one, one comma. Infinity Report. Be so we're gonna see that that X is equal to negative one. It goes from decreasing to increasing, so it's a minimum and X equals one. It goes from increasing to decreasing, so it's a maximum. Now we're gonna find the second derivative, which is equal to 30 X minus 60 x cubed. We're gonna find where it's equal to zero and we get X is equal to zero. X is equal to plus or minus one over square root of two. So we're gonna first look up the interval. Negative. Infinity. Pullman Negative One over square root of two. We choose negative one. And what bigger than zero Since h of negative one is bigger than zero, it's actually 30. We go negative one over square root of two comma zero. We look at the second derivative of negative 0.1. This is less than zero. You look from zero comma, one over square root of two, and we choose 0.1, which is bigger than zero. And finally we look at one over square root of two to infinity, and we look at one which is less than zero. We clung it in to the regular equation when yet negative 1.237 for each of 00 for H of one over square root of two. That is around 1.237 So we get inflection points to be negative. One over square root of two common negative 1.237 zero comma zero and one of her skirt of two comma 1.237 Next, we're gonna draw a quick for us, and it looks something like this

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
154
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

04:36

(a) Find the intervals of increase or decrease. (b) Find the local maximum and…

0:00

(a) Find the intervals of increase or decrease. (b) Find the local maximum and…

05:23

(a) Find the intervals of increase or decrease. (b) Find the local maximum and …

02:09

(a) Find the intervals of increase or decrease. (b) Find the local maximum and…

01:47

(a) Find the intervals of increase or decrease. (b) Find the local maximum and…

0:00

(a) Find the intervals of increase or decrease. (b) Find the local maximum and…

04:02

(a) Find the intervals of increase or decrease. (b) Find the local maximum and…

03:14

(a) Find the intervals of increase or decrease. (b) Find the local maximum and…

05:23

(a) Find the intervals of increase or decrease. (b) Find the local maximum and …

05:23

(a) Find the intervals of increase or decrease. (b) Find the local maximum and …

0:00

(a) Find the intervals of increase or decrease. (b) Find the local maximum and…

02:43

(a) Find the intervals of increase or decrease. (b) Find the local maximum and…

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