Explanation Calculation: The function is, f ( x ) = x ( x − 6 ) The interval is [ 1 , 5 ] Consider the following figure of the function. From above figure, it is clear that the function in continuous on [ 1 , 5 ] . Therefore, the mean value theorem for integrals is applicable to the above function. The objective is to state the conclusion of the mean value theorem for integrals for the above function. The conclusion is that there exists some point c ∈ ( a , b ) such that f ( c ) = 1 b − a ∫ a b f ( x ) d x The average value is, f ( c ) = 1

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 4.6, Problem 21C

To determine

Toexplain: The mean value theorem for integrals applies to the function f(x)=x(x−6) on the interval [1,5] .To state the conclusion of the mean value theorem for integrals in this particular case, and sketch a graph illustrating your conclusion. To find all the values c∈[1,5] for which f(c) is equal to the average value of f on [1,5] , and indicate these values on your graph.

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Chapter 4.6, Problem 20C

Chapter 4.6, Problem 22C

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Solution Summary: The author states the conclusion of the mean value theorem for integrals for the above function.

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