(A) Explanation Formula used: Average value of a function : The average value of a continuous function f over [ a , b ] can be calculated by 1 b − a ∫ a b f ( x ) d x . Calculation: The function is given as g ( t ) = 4 t − 3 t 2 . Since the function is defined over the interval [ − 2 , 2 ] , the average value can be calculated as follows. Average value = 1 b − a ∫ a b g ( t ) d t = 1 2 − ( − 2 ) ∫ − 2 2 ( 4 t − 3 t 2 ) d t = 1 4 [ 4 ( (B) To determine To graph: The function g ( t ) = 4 t − 3 t 2 and indicate the average value over the interval [ − 2 , 2 ] .

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134674148

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

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Chapter 12.5, Problem 52E

(A)

To determine

To find: The average value of the function g(t)=4t−3t2 over the interval [−2,2].

(B)

To determine

To graph: The function g(t)=4t−3t2 and indicate the average value over the interval [−2,2].

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Chapter 12.5, Problem 51E

Chapter 12.5, Problem 53E

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Chapter 12 Solutions

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 12.1 - Matched Problem 1 Note that Find all...Ch. 12.1 - Prob. 2MP Ch. 12.1 - Prob. 3MP Ch. 12.1 - Prob. 4MP Ch. 12.1 - Prob. 5MP Ch. 12.1 - Prob. 6MP Ch. 12.1 - Prob. 1ED Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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The average value of the function g ( t ) = 4 t − 3 t 2 over the interval [ − 2 , 2 ] .

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To find: The average value of the function g(t)=4t−3t2 over the interval [−2,2].

To graph: The function g(t)=4t−3t2 and indicate the average value over the interval [−2,2].

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Chapter 12 Solutions