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

What is the shortest possible length of the line …

04:55

Question

Answered step-by-step

Problem 56 Hard Difficulty

At which points on the curve $ y = 1 + 40x^3 - 3x^5 $ does the tangent line have the largest slope?


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Linda Hand
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Linda Hand

Numerade Educator

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

More Answers

03:52

WZ

Wen Zheng

01:30

Amrita Bhasin

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 7

Optimization Problems

Related Topics

Derivatives

Differentiation

Volume

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Michael Jacobsen

Idaho State University

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

0:00

At which points on the cur…

03:22

At which points on the cur…

01:57

Where on the curve $y=\lef…

03:15

Where on the curve $y=\fra…

01:17

What is the smallest possi…

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 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

Video Transcript

equals one plus 40 X cubed minus three X to the fifth. Does the tangent line have the largest? Look. Okay, so largest. We're gonna maximize something. Gonna maximize slope of the tangent line. All right? And to find the slope of the tangent line, we have to take the derivative. So m tan. Because why prime, which is 1 20 X square minus 15 x to the fourth. Okay, now, we're not gonna set that equal to zero because we're not looking for the tangent is equal to zero or looking for the maximum tangent. So we have to take the derivative of it in 10. Prime. So to 40 x minus 60 x cubed equals zero. We confected out of 60 x and we get four minus x squared. So X is plus or minus two. And so then why is one plus 40 times two cubed minus three times to to the fifth tomorrow. Plus too cute 40 minus 12 one. Plus, um, maybe why don't I just do this on my calculator? That might be easier. Okay, let's see now. You know what? I can do that to Cuba today. Eight times 43. 20 to do the 5th, 32 32 times 3 96. So 3. 21 minus 96 five two. So 2. 25. So two comma 2 25. And then if you put a minus in there, it's minus 3 28 plus 96. So it will be 3. 20 minus 97. So three forever tu minus 2 23 minus 2 a.m. minus 2. 23.

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
142
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
Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Michael Jacobsen

Idaho State University

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

0:00

At which points on the curve $ y = 1 + 40x^3 - 3x^5 $ does the tangent line hav…

03:22

At which points on the curve $y=1+40 x^{3}-3 x^{5}$ does the tangent line have …

01:57

Where on the curve $y=\left(1+x^{2}\right)^{-1}$ does the tangent line have the…

03:15

Where on the curve $y=\frac{1}{1+x^{2}}$ does the tangent line have the greates…

01:17

What is the smallest possible slope for a tangent to the graph of the equation …

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