Solved: Let f(v) be the gas consumption (in liters/km) of a cargoing at velocity v (in

Chapter 3, Problem 59

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Let f(v) be the gas consumption (in liters/km) of a cargoing at velocity v (in km/hr). In other words, f(v) tellsyou how many liters of gas the car uses to go one kilometer,if it is going at velocity v. You are told thatf(80) = 0.05 and f(80) = 0.0005.(a) Let g(v) be the distance the same car goes on oneliter of gas at velocity v. What is the relationship betweenf(v) and g(v)? Find g(80) and g(80).(b) Let h(v) be the gas consumption in liters per hour.In other words, h(v) tells you how many liters ofgas the car uses in one hour if it is going at velocityv. What is the relationship between h(v) and f(v)?Find h(80) and h(80).(c) How would you explain the practical meaning of thevalues of these functions and their derivatives to adriver who knows no calculus?

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