Activity 1.5.4.
Researchers at a major car company have found a function that relates gasoline consumption to speed for a particular model of car. In particular, they have determined that the consumption \(C\text{,}\) in liters per kilometer, at a given speed \(s\text{,}\) is given by a function \(C = f(s)\text{,}\) where \(s\) is the car’s speed in kilometers per hour.
(a)
Data provided by the car company tells us that \(f(80) = 0.015\text{,}\) \(f(90) = 0.02\text{,}\) and \(f(100) = 0.027\text{.}\) Use this information to estimate the instantaneous rate of change of fuel consumption with respect to speed at \(s = 90\text{.}\) Be as accurate as possible, use proper notation, and include units on your answer.
(b)
By writing a complete sentence, interpret the meaning (in the context of fuel consumption) of “\(f(80) = 0.015\text{.}\)”
(c)
Write at least one complete sentence that interprets the meaning of the value of \(f'(90)\) that you estimated in (a).
