Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

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

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Kian Manafi

Numerade Educator

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

02:54

Fahad Paryani

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

Derivatives

Differentiation

Volume

University of Michigan - Ann Arbor

University of Nottingham

Boston College

Lectures

04:35

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.

06:14

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.

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

01:14

If $k_{\mathrm{f}}>k_{\…

02:32

Figure 4.118 shows the gra…

Explain why the graph of $…

00:46

01:23

Use the derivative test in…

00:56

00:18

Decide whether the graph i…

00:10

00:25

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.

View More Answers From This Book

Find Another Textbook

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

20Find 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

McMapsYouTubeXEvaluate: 268 4400 156/366

03:52

Consider the function flx) = 3e` rFind 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…