Explanation Given: The distance covered by person L in 78 minutes is 22 miles . Concept used: The mean value theorem: The mean value theorem states that if the function f is continuous on the interval [ a , b ] and differentiable on the interval ( a , b ) then a number c exists in the interval such that the slope at c can be expressed as follows: f ′ ( c ) = f ( b ) − f ( a ) b − a ..... (1) Calculation: The time taken to covered the distance 22 miles is 78 minute . In an hour there are 60 minutes . 60 minute = 1 hour Convert 78 minute in to hours as shown below. 78 minute = 78 60 hour =1 .3 hour The derivative of distance with respect to time gives the velocity. Consider 0 as a , 1

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 4.3, Problem 64E

To determine

To explain:

The use of Mean Value Theorem that support the complaint of person L.

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Chapter 4.3, Problem 63E

Chapter 4.3, Problem 65E

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Two days after he bought a speedometer for his bicycle, Lance brought it back to the Yellow Jersey Bike Shop. “There is a problem with this speedometer," Lance complained to the clerk. “Yesterday I cycled the 22-mile Rogadzo Road Trail in 77 minutes, and not once did the speedometer read above 15 miles per hour!" "Yeah?" responded the clerk. "What's the problem?" To explain Lance's complaint, first compute his average velocity. (Use decimal notation. Give your answer to two decimal places.) average velocity: miles/hour How did Lance use the Mean Value Theorem to explain his complaint? For 50% of time, Lance's speed exceeds his average speed that in turn is above 15 miles/hour. As Lance's average speed is greater than 15 miles/hour, at any moment of time the speedometer should show the speed that is above 15 miles/hour. There is at least one moment of time when Lance's speed is equal to his average speed. At that moment Lance's speed exceeds the speed of 15 miles/hour.

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Chapter 4 Solutions

Calculus: Early Transcendentals

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The use of Mean Value Theorem that support the complaint of person L.

Solution Summary: The author explains the use of the mean value theorem that support the complaint of person L.

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To explain: The use of Mean Value Theorem that support the complaint of person L.

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To explain:

The use of Mean Value Theorem that support the complaint of person L.