Problem

Coffee is being poured into the mug shown in the …

02:13

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?

Name: let kt be a measure of the knowledge you gain by studying for a test for t hours which do you think
Uploaded: 2021-05-13
Duration: 1 min 48 s
Channel: Numerade
Description: 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?

Answer

Most students learn more in the third hour of studying than in the eighth hour, so $K(3)-K(2)$ is larger than $K(8)-K(7)$
In other words, as you begin studying for a test, the rate of knowledge gain is large and then starts to taper off, so $K^{\prime}(t)$
decreases and the graph of $K$ is concave downward.

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Grace H.

Anna Marie V.

Campbell University

Caleb E.

Baylor University

Michael J.

Idaho State University

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

Problem 83

Problem 84

Problem 85

Problem 86

Problem 87

Problem 88

Problem 89

Problem 90

Problem 91

Problem 92

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.

Kian M.

Oregon State University

Topics

Derivatives

Differentiation

Volume

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph