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 $C$, in liters per kilometer, at a given speed $s$, is given by a function $C = f(s)$, where $s$ is the car's speed in kilometers per hour.

1. 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.

2. By writing a complete sentence, interpret the meaning (in the context of fuel consumption) of “$f(80) = 0.015$.”

3. Write at least one complete sentence that interprets the meaning of the value of $f'(90)$ that you estimated in (a).