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

Coffee is being poured into the mug shown in the …
02:13

Question

Answered step-by-step

Problem 69 Hard Difficulty

Let $ K(t) $ be a measure of the knowledge you gain by studying for a test for $ t $ hours. Which do you think is larger, $ K(8) - K(7) $ or $ K(3) - K(2) $? Is the graph of $ K $ concave upward or concave downward? Why?

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

02:54

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
Grace He
Kristen Karbon

University of Michigan - Ann Arbor

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

01:03

Let $K(t)$ be a measure of…

00:42

Refer to the values of $a,…

01:30

Use a graph to estimate th…

00:32

Refer to the values of $a,…

01:14

If $k_{\mathrm{f}}>k_{\…

02:32

Figure 4.118 shows the gra…

00:42

Explain why the graph of $…

00:46

Refer to the values of $a,…

01:23

Use the derivative test in…

00:56

Use the derivative test in…

00:18

Decide whether the graph i…

00:10

Decide whether the graph i…

00:10

Decide whether the graph i…

00:25

Decide whether the graph i…

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

But we're told that KFT tells us the knowledge gained after tea hours of studying and we want to figure out if K. Of eight minus K. Of seven. So the knowledge gained after eight hours minus the knowledge gained after seven hours. If this is greater than or equal to the knowledge gained after three hours minus the knowledge gained after two hours. So the way that we want to think about this is when you're studying it seems like we get at the beginning we're studying and we're increasing in terms of our knowledge. Our knowledge is increasing at a higher rate after three hours versus after eight hours after eight hours of studying you're going to be increasing your knowledge but it's going to be less and less of a big increase than after three hours. So after three hours minus the knowledge after two hours, this is actually gonna be bigger than the increase from eight to seven hours. Since the increase in knowledge studying from three hours to two hours is a lot bigger than the increase from seven hours to eight hours. So this one K over three minus or K. Of three minus cave to is going to be bigger than cave eight -K. of seven. And now we want to figure out if we're concave up or concave down, well, we know that we are increasing our knowledge at a decreasing rate. So our first derivative K. Prime of T. That's still going to be positive since we're increasing however, were increasing at a decreasing rate. So our second derivative is going to be negative, which means that we are going to be concave down. So this graph cave cave T. Is going to be concave down. All right.

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
95
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
54
Hosted by: Alonso M
See More

Related Topics

Derivatives

Differentiation

Volume
Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Kristen Karbon

University of Michigan - Ann Arbor

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

01:03

Let $K(t)$ be a measure of the knowledge you gain by studying for a test for $t…

00:42

Refer to the values of $a, h,$ and $k$ in the vertex form of a quadratic functi…

01:30

Use a graph to estimate the local extrema and inflection points of each functio…

00:32

Refer to the values of $a, h,$ and $k$ in the vertex form of a quadratic functi…

01:14

If $k_{\mathrm{f}}>k_{\mathrm{r}}$, will $K_{\mathrm{eq}}$ be less than 1 or gr…

02:32

Figure 4.118 shows the graph of a parameterized curve $x=f(t), y=f^{\prime}(t)$…

00:42

Explain why the graph of $y=f(x)+k$ is the same as the graph of $y=f(x)$ moved …

00:46

Refer to the values of $a, h,$ and $k$ in the vertex form of a quadratic functi…

01:23

Use the derivative test in Theorem 7.6 to analyze the monotonicity of the given…

00:56

Use the derivative test in Theorem $7.6$ to analyze the monotonicity of the giv…

00:18

Decide whether the graph is concave up, concave down, or neither.

00:10

Decide whether the graph is concave up, concave down, or neither.

00:10

Decide whether the graph is concave up, concave down, or neither.

00:25

Decide whether the graph is concave up, concave down, or neither.
Additional Mathematics Questions

02:11

answer the following; by inspection graph ofy f(x) , shown below Given (0.5 …

02:59

Using the value function v(x) Vx over gains and v(x) 2Vlx| over losses: Desi…

03:50

14. The American Heart Association recommends a daily cholesterol intake of …

09:00

20
Find the inverses (in any legal way) of 0 0 0 2 8] N 0 Lo 0 0 3 0 4 3 …

04:36

Spade Realty sold lots for $23 240 per hectare. What is the total sales valu…

02:41

Complete the following word problems: The graph at the right shows the volum…

03:42

Mc
Maps
YouTube
X
Evaluate: 268 4400 156/366

03:52

Consider the function flx) = 3e` r
Find the following sets and values Ent…

01:45

Brooks Insurance Inc. wishes to offer life insurance to men age 60 via the I…

04:26

An emergency unit has three ambulances; A1,AZ, and A3; operating independent…

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