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, in liters per kilometer, at a given speed s, is given by a function C = f (s), where s is the car speed in kilometers per hour.
(a) Data provided by the car company tells us that f (80) = 0.015, f (90) = 0.02, and f (100) = 0.027.
Use this information to estimate the instantaneous rate of change of fuel consumption with respect to speed at s = 90.
Be as accurate as possible, use proper notation, and include units on your answer.