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4. At Wally Motors, an auto engineer, in testing a new engine on one of its new models, found that the efficiency e of the engine as a function of the speed s of the car was given by e= 0.768s – 0.00004s. Here e is measured in percent and s is measured in km/hr. What is the maximum efficiency of the engine?

4. At Wally Motors, an auto engineer, in testing a new engine on one of its new models, found that the efficiency e of the engine as a function of the speed s of the car was given by e= 0.768s – 0.00004s. Here e is measured in percent and s is measured in km/hr. What is the maximum efficiency of the engine?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem 4: Calculating Maximum Engine Efficiency** At Wally Motors, an automotive engineer conducted tests on a new engine for one of their latest car models. The tests determined that the engine's efficiency \( e \), as a function of the car's speed \( s \), is represented by the equation: \[ e = 0.768s - 0.00004s^3 \] In this context: - \( e \) is the efficiency measured in percent. - \( s \) is the speed measured in kilometers per hour (km/hr). **Question:** What is the maximum efficiency that the engine can achieve? --- To find the maximum efficiency, you would typically take the derivative of the function \( e(s) = 0.768s - 0.00004s^3 \) with respect to \( s \), set it to zero, and solve for \( s \). This will identify the speed at which the efficiency is maximized.
Transcribed Image Text:**Problem 4: Calculating Maximum Engine Efficiency** At Wally Motors, an automotive engineer conducted tests on a new engine for one of their latest car models. The tests determined that the engine's efficiency \( e \), as a function of the car's speed \( s \), is represented by the equation: \[ e = 0.768s - 0.00004s^3 \] In this context: - \( e \) is the efficiency measured in percent. - \( s \) is the speed measured in kilometers per hour (km/hr). **Question:** What is the maximum efficiency that the engine can achieve? --- To find the maximum efficiency, you would typically take the derivative of the function \( e(s) = 0.768s - 0.00004s^3 \) with respect to \( s \), set it to zero, and solve for \( s \). This will identify the speed at which the efficiency is maximized.
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