Let f(v) be the gas consumption (in liters/kilometer) of a car going at velocity

Question

Let f(v) be the gas consumption (in liters/kilometer) of a car going at velocity v (kilo- meters/hour). In other words, f(v) tells you how many liters of gas the car uses to go one kilometer when traveling at velocity v. You are told that f(80) = 0.05 and f?(80) = 0.005 Question 1: Let g(v) be the distance the same car goes on one liter of gas at velocity v. What is the relationship between f(v) and g(v)? Find g(80) and g?(80). Question 2: Let h(v) be the gas consumption of the same car in liters per hour. In other words, h(v) tells you how many liters the car uses in one hour if it is going at a velocity v. What is the relationship between f(v) and h(v)? Find h(80) and h?(80). Question 3: How would you explain the practical meaning of the values of these functions and their derivatives to a driver who knows no calculus?

Explanation / Answer

f(v) * g(v) = 1. You need the velocity to calcuate h(v) outgoing from f(v) . h(v) ist used for engine construction and has no great meaning for drivers.

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