Chapter 3.3, Problem 59E

Let f(υ) be the gas consumption (in liters/km) of a car going at velocity v (in km/hr). In other words, f(υ) tells you how many liters of gas the car uses to go one kilometer, if it is going at velocity v. You are told that

$f(80)=0.05and{f}^{\prime }(80)=0.0005$

1. (a) Let g(υ) be the distance the same car goes on one liter of gas at velocity v. What is the relationship between f(υ)and g(υ)? Find g(80) and g′ (80).
2. (b) Let h(υ) be the gas consumption in liters per hour. In other words, h(υ) tells you how many liters of gas the car uses in one hour if it is going at velocity v. What is the relationship between h(υ) and f(υ)? Find h(80) and h′(80).
3. (c) How would you explain the practical meaning of the values of these functions and their derivatives to a driver who knows no calculus?