EBK ALGEBRA 2
EBK ALGEBRA 2
11th Edition
ISBN: 9780544714304
Author: Larson
Publisher: HMH PUB
Expert Solution & Answer
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Chapter 5.7, Problem 32PS
Solution

a.

To determine: the average rate of change of the function over the intervals 0,1,1,2,2,3,and3,4 .

The average rate of change of the function over the intervals 0,1,1,2,2,3,and3,4 are 224,56,64and136 .

Given information:

The volume V of the box is V=x182x184x

Concept Used:

Average rate of change:

The average rate of change of a function fx over an interval a,b is defined as the ratio of "change in the function values" to the "change in the endpoints of the interval". i.e., the average rate of change can be calculated using fbfaba .

Calculation:

Evaluate the value of V0,V1,V2andV3 .

  V0=0182(0)184(0)=0V1=1182(1)184(1)=224V2=2182(2)184(2)=280V3=3182(3)184(3)=216V4=4182(4)184(4)=80

The average rate of change of the function over the intervals 0,1 are 224010=224 .

The average rate of change of the function over the intervals 1,2 are 28022421=56 .

The average rate of change of the function over the intervals 2,3 are 21628032=64 .

The average rate of change of the function over the intervals 3,4 are 8021643=136 .

b.

To determine: the maximum and minimum value occur over any intervals in part(a).

The maximum value is 224 over the interval of 0,1 .

The minimum value is 136 over the interval of 4,3 .

Given information:

The volume V of the box is V=x182x184x

Concept Used:

Average rate of change:

The average rate of change of a function fx over an interval a,b is defined as the ratio of "change in the function values" to the "change in the endpoints of the interval". i.e., the average rate of change can be calculated using fbfaba .

Calculation:

The average rate of change of the function over the intervals 0,1 are 224010=224 .

The average rate of change of the function over the intervals 1,2 are 28022421=56 .

The average rate of change of the function over the intervals 2,3 are 21628032=64 .

The average rate of change of the function over the intervals 3,4 are 8021643=136 .

From the above, it is observed that the maximum and minimum values occur in the interval 0,1 and 3,4

Chapter 5 Solutions

EBK ALGEBRA 2

Ch. 5.1 - Prob. 11GPCh. 5.1 - Prob. 12GPCh. 5.1 - Prob. 13GPCh. 5.1 - Prob. 14GPCh. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10ECh. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37PSCh. 5.1 - Prob. 38PSCh. 5.1 - Prob. 39PSCh. 5.1 - Prob. 40PSCh. 5.1 - Prob. 41PSCh. 5.1 - Prob. 42PSCh. 5.2 - Prob. 1GPCh. 5.2 - Prob. 2GPCh. 5.2 - Prob. 3GPCh. 5.2 - Prob. 4GPCh. 5.2 - Prob. 5GPCh. 5.2 - Prob. 6GPCh. 5.2 - Prob. 7GPCh. 5.2 - Prob. 1ECh. 5.2 - Prob. 2ECh. 5.2 - Prob. 3ECh. 5.2 - Prob. 4ECh. 5.2 - Prob. 5ECh. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 - Prob. 10ECh. 5.2 - Prob. 11ECh. 5.2 - Prob. 12ECh. 5.2 - Prob. 13ECh. 5.2 - Prob. 14ECh. 5.2 - Prob. 15ECh. 5.2 - Prob. 16ECh. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - Prob. 19ECh. 5.2 - Prob. 20ECh. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Prob. 23ECh. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - Prob. 26ECh. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.2 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 37PSCh. 5.2 - Prob. 38PSCh. 5.2 - Prob. 39PSCh. 5.2 - Prob. 40PSCh. 5.2 - Prob. 41PSCh. 5.2 - Prob. 42PSCh. 5.2 - Prob. 1PCh. 5.2 - Prob. 2PCh. 5.2 - Prob. 3PCh. 5.2 - Prob. 4PCh. 5.2 - Prob. 5PCh. 5.2 - Prob. 6PCh. 5.2 - Prob. 7PCh. 5.2 - Prob. 8PCh. 5.2 - Prob. 9PCh. 5.2 - Prob. 1.1PCh. 5.2 - Prob. 1.2PCh. 5.2 - Prob. 1.3PCh. 5.2 - Prob. 1.4PCh. 5.2 - Prob. 1.5PCh. 5.2 - Prob. 1.6PCh. 5.2 - Prob. 1.7PCh. 5.2 - Prob. 1.8PCh. 5.2 - Prob. 1.9PCh. 5.2 - Prob. 1.10PCh. 5.3 - Prob. 1GPCh. 5.3 - Prob. 2GPCh. 5.3 - Prob. 3GPCh. 5.3 - Prob. 4GPCh. 5.3 - Prob. 5GPCh. 5.3 - Prob. 1ECh. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prob. 5ECh. 5.3 - Prob. 6ECh. 5.3 - Prob. 7ECh. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31PSCh. 5.3 - Prob. 32PSCh. 5.3 - Prob. 33PSCh. 5.3 - Prob. 34PSCh. 5.3 - Prob. 35PSCh. 5.3 - Prob. 36PSCh. 5.3 - Prob. 1QCh. 5.3 - Prob. 2QCh. 5.3 - Prob. 3QCh. 5.3 - Prob. 4QCh. 5.3 - Prob. 5QCh. 5.3 - Prob. 6QCh. 5.3 - Prob. 7QCh. 5.3 - Prob. 8QCh. 5.3 - Prob. 9QCh. 5.3 - Prob. 10QCh. 5.3 - Prob. 11QCh. 5.3 - Prob. 1MRPSCh. 5.3 - Prob. 2MRPSCh. 5.3 - Prob. 3MRPSCh. 5.3 - Prob. 4MRPSCh. 5.3 - Prob. 5MRPSCh. 5.3 - Prob. 6MRPSCh. 5.3 - Prob. 7MRPSCh. 5.3 - Prob. 8MRPSCh. 5.4 - Prob. 1GPCh. 5.4 - Prob. 2GPCh. 5.4 - Prob. 3GPCh. 5.4 - Prob. 4GPCh. 5.4 - Prob. 5GPCh. 5.4 - Prob. 6GPCh. 5.4 - Prob. 7GPCh. 5.4 - Prob. 8GPCh. 5.4 - Prob. 9GPCh. 5.4 - Prob. 10GPCh. 5.4 - Prob. 11GPCh. 5.4 - Prob. 12GPCh. 5.4 - Prob. 1ECh. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Prob. 10ECh. 5.4 - Prob. 11ECh. 5.4 - Prob. 12ECh. 5.4 - Prob. 13ECh. 5.4 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - Prob. 19ECh. 5.4 - Prob. 20ECh. 5.4 - Prob. 21ECh. 5.4 - Prob. 22ECh. 5.4 - Prob. 23ECh. 5.4 - Prob. 24ECh. 5.4 - Prob. 25ECh. 5.4 - Prob. 26ECh. 5.4 - Prob. 27ECh. 5.4 - Prob. 28ECh. 5.4 - Prob. 29ECh. 5.4 - Prob. 30ECh. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.4 - Prob. 45ECh. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48PSCh. 5.4 - Prob. 49PSCh. 5.4 - Prob. 50PSCh. 5.4 - Prob. 51PSCh. 5.4 - Prob. 52PSCh. 5.4 - Prob. 53PSCh. 5.4 - Prob. 1PCh. 5.4 - Prob. 2PCh. 5.4 - Prob. 3PCh. 5.4 - Prob. 4PCh. 5.4 - Prob. 5PCh. 5.4 - Prob. 6PCh. 5.5 - Prob. 1GPCh. 5.5 - Prob. 2GPCh. 5.5 - Prob. 3GPCh. 5.5 - Prob. 4GPCh. 5.5 - Prob. 5GPCh. 5.5 - Prob. 6GPCh. 5.5 - Prob. 7GPCh. 5.5 - Prob. 8GPCh. 5.5 - Prob. 9GPCh. 5.5 - Prob. 10GPCh. 5.5 - Prob. 11GPCh. 5.5 - Prob. 12GPCh. 5.5 - Prob. 13GPCh. 5.5 - Prob. 1ECh. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.5 - Prob. 6ECh. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.5 - Prob. 10ECh. 5.5 - Prob. 11ECh. 5.5 - Prob. 12ECh. 5.5 - Prob. 13ECh. 5.5 - Prob. 14ECh. 5.5 - Prob. 15ECh. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - Prob. 20ECh. 5.5 - Prob. 21ECh. 5.5 - Prob. 22ECh. 5.5 - Prob. 23ECh. 5.5 - Prob. 24ECh. 5.5 - Prob. 25ECh. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - Prob. 28ECh. 5.5 - Prob. 29ECh. 5.5 - Prob. 30ECh. 5.5 - Prob. 31ECh. 5.5 - Prob. 32ECh. 5.5 - Prob. 33ECh. 5.5 - Prob. 34ECh. 5.5 - Prob. 35ECh. 5.5 - Prob. 36ECh. 5.5 - Prob. 37ECh. 5.5 - Prob. 38ECh. 5.5 - Prob. 39ECh. 5.5 - Prob. 40ECh. 5.5 - Prob. 41PSCh. 5.5 - Prob. 42PSCh. 5.5 - Prob. 43PSCh. 5.5 - Prob. 44PSCh. 5.5 - Prob. 45PSCh. 5.5 - Prob. 1PCh. 5.5 - Prob. 2PCh. 5.5 - Prob. 3PCh. 5.5 - Prob. 4PCh. 5.5 - Prob. 5PCh. 5.5 - Prob. 6PCh. 5.5 - Prob. 7PCh. 5.6 - Prob. 1GPCh. 5.6 - Prob. 2GPCh. 5.6 - Prob. 3GPCh. 5.6 - Prob. 4GPCh. 5.6 - Prob. 5GPCh. 5.6 - Prob. 6GPCh. 5.6 - Prob. 7GPCh. 5.6 - Prob. 8GPCh. 5.6 - Prob. 9GPCh. 5.6 - Prob. 10GPCh. 5.6 - Prob. 11GPCh. 5.6 - Prob. 1ECh. 5.6 - Prob. 2ECh. 5.6 - Prob. 3ECh. 5.6 - Prob. 4ECh. 5.6 - Prob. 5ECh. 5.6 - Prob. 6ECh. 5.6 - Prob. 7ECh. 5.6 - Prob. 8ECh. 5.6 - Prob. 9ECh. 5.6 - Prob. 10ECh. 5.6 - Prob. 11ECh. 5.6 - Prob. 12ECh. 5.6 - Prob. 13ECh. 5.6 - Prob. 14ECh. 5.6 - Prob. 15ECh. 5.6 - Prob. 16ECh. 5.6 - Prob. 17ECh. 5.6 - Prob. 18ECh. 5.6 - Prob. 19ECh. 5.6 - Prob. 20ECh. 5.6 - Prob. 21ECh. 5.6 - Prob. 22ECh. 5.6 - Prob. 23ECh. 5.6 - Prob. 24ECh. 5.6 - Prob. 25ECh. 5.6 - Prob. 26ECh. 5.6 - Prob. 27ECh. 5.6 - Prob. 28ECh. 5.6 - Prob. 29ECh. 5.6 - Prob. 30ECh. 5.6 - Prob. 31ECh. 5.6 - Prob. 32ECh. 5.6 - Prob. 33PSCh. 5.6 - Prob. 34PSCh. 5.6 - Prob. 35PSCh. 5.6 - Prob. 36PSCh. 5.6 - Prob. 37PSCh. 5.6 - Prob. 38PSCh. 5.6 - Prob. 1QCh. 5.6 - Prob. 2QCh. 5.6 - Prob. 3QCh. 5.6 - Prob. 4QCh. 5.6 - Prob. 5QCh. 5.6 - Prob. 6QCh. 5.6 - Prob. 7QCh. 5.6 - Prob. 8QCh. 5.6 - Prob. 9QCh. 5.6 - Prob. 10QCh. 5.6 - Prob. 11QCh. 5.6 - Prob. 12QCh. 5.6 - Prob. 13QCh. 5.6 - Prob. 14QCh. 5.6 - Prob. 1PCh. 5.6 - Prob. 2PCh. 5.6 - Prob. 3PCh. 5.6 - Prob. 4PCh. 5.6 - Prob. 5PCh. 5.6 - Prob. 6PCh. 5.6 - Prob. 7PCh. 5.6 - Prob. 1.1PCh. 5.6 - Prob. 1.2PCh. 5.6 - Prob. 1.3PCh. 5.6 - Prob. 1.4PCh. 5.6 - Prob. 1.5PCh. 5.6 - Prob. 1.6PCh. 5.6 - Prob. 1.7PCh. 5.6 - Prob. 1.8PCh. 5.6 - Prob. 1.9PCh. 5.6 - Prob. 1.10PCh. 5.6 - Prob. 1.11PCh. 5.6 - Prob. 1.12PCh. 5.6 - Prob. 1.13PCh. 5.6 - Prob. 1.14PCh. 5.6 - Prob. 1.15PCh. 5.6 - Prob. 1.16PCh. 5.6 - Prob. 1.17PCh. 5.6 - Prob. 1.18PCh. 5.6 - Prob. 1.19PCh. 5.6 - Prob. 1.20PCh. 5.6 - Prob. 1.21PCh. 5.6 - Prob. 1.22PCh. 5.7 - Prob. 1GPCh. 5.7 - Prob. 2GPCh. 5.7 - Prob. 3GPCh. 5.7 - Prob. 4GPCh. 5.7 - Prob. 5GPCh. 5.7 - Prob. 1ECh. 5.7 - Prob. 2ECh. 5.7 - Prob. 3ECh. 5.7 - Prob. 4ECh. 5.7 - Prob. 5ECh. 5.7 - Prob. 6ECh. 5.7 - Prob. 7ECh. 5.7 - Prob. 8ECh. 5.7 - Prob. 9ECh. 5.7 - Prob. 10ECh. 5.7 - Prob. 11ECh. 5.7 - Prob. 12ECh. 5.7 - Prob. 13ECh. 5.7 - Prob. 14ECh. 5.7 - Prob. 15ECh. 5.7 - Prob. 16ECh. 5.7 - Prob. 17ECh. 5.7 - Prob. 18ECh. 5.7 - Prob. 19ECh. 5.7 - Prob. 20ECh. 5.7 - Prob. 21ECh. 5.7 - Prob. 22ECh. 5.7 - Prob. 23ECh. 5.7 - Prob. 24ECh. 5.7 - Prob. 25ECh. 5.7 - Prob. 26PSCh. 5.7 - Prob. 27PSCh. 5.7 - Prob. 28PSCh. 5.7 - Prob. 29PSCh. 5.7 - Prob. 30PSCh. 5.7 - Prob. 31PSCh. 5.7 - Prob. 32PSCh. 5.7 - Prob. 1QCh. 5.7 - Prob. 2QCh. 5.7 - Prob. 3QCh. 5.7 - Prob. 4QCh. 5.7 - Prob. 5QCh. 5.7 - Prob. 1MRPSCh. 5.7 - Prob. 2MRPSCh. 5.7 - Prob. 3MRPSCh. 5.7 - Prob. 4MRPSCh. 5.7 - Prob. 5MRPSCh. 5.7 - Prob. 6MRPSCh. 5.7 - Prob. 7MRPSCh. 5 - Prob. 1VECh. 5 - Prob. 2VECh. 5 - Prob. 3VECh. 5 - Prob. 4VECh. 5 - Prob. 5VECh. 5 - Prob. 6REAECh. 5 - Prob. 7REAECh. 5 - Prob. 8REAECh. 5 - Prob. 9REAECh. 5 - Prob. 10REAECh. 5 - Prob. 11REAECh. 5 - Prob. 12REAECh. 5 - Prob. 13REAECh. 5 - Prob. 14REAECh. 5 - Prob. 15REAECh. 5 - Prob. 16REAECh. 5 - Prob. 17REAECh. 5 - Prob. 18REAECh. 5 - Prob. 19REAECh. 5 - Prob. 20REAECh. 5 - Prob. 21REAECh. 5 - Prob. 22REAECh. 5 - Prob. 23REAECh. 5 - Prob. 24REAECh. 5 - Prob. 25REAECh. 5 - Prob. 26REAECh. 5 - Prob. 27REAECh. 5 - Prob. 28REAECh. 5 - Prob. 29REAECh. 5 - Prob. 30REAECh. 5 - Prob. 31REAECh. 5 - Prob. 32REAECh. 5 - Prob. 33REAECh. 5 - Prob. 1TCh. 5 - Prob. 2TCh. 5 - Prob. 3TCh. 5 - Prob. 4TCh. 5 - Prob. 5TCh. 5 - Prob. 6TCh. 5 - Prob. 7TCh. 5 - Prob. 8TCh. 5 - Prob. 9TCh. 5 - Prob. 10TCh. 5 - Prob. 11TCh. 5 - Prob. 12TCh. 5 - Prob. 13TCh. 5 - Prob. 14TCh. 5 - Prob. 15TCh. 5 - Prob. 16TCh. 5 - Prob. 17TCh. 5 - Prob. 18TCh. 5 - Prob. 19TCh. 5 - Prob. 20TCh. 5 - Prob. 21TCh. 5 - Prob. 22TCh. 5 - Prob. 23TCh. 5 - Prob. 24TCh. 5 - Prob. 25TCh. 5 - Prob. 26TCh. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 1TPCh. 5 - Prob. 2TPCh. 5 - Prob. 3TPCh. 5 - Prob. 4TPCh. 5 - Prob. 5TPCh. 5 - Prob. 6TPCh. 5 - Prob. 7TPCh. 5 - Prob. 8TPCh. 5 - Prob. 9TPCh. 5 - Prob. 10TPCh. 5 - Prob. 11TPCh. 5 - Prob. 12TPCh. 5 - Prob. 13TPCh. 5 - Prob. 14TPCh. 5 - Prob. 15TPCh. 5 - Prob. 16TPCh. 5 - Prob. 17TP
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