Let f(v) be the gas consumption (L/km) of a car going at velocity v (km/h). In other words, f(v) 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) = 0.05 and f`(80) = 0.0005.
a) 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).
Okay, I'm pretty sure their relationship is: g(v) = f^-1(v). I tried to find the value of g(80) and came out with the pretty ridiculous value of 159980km/L. I am almost certain I did this wrong, but I can't find any relevant info in my textbook. For g`(80) I know I have to use the inverse rule to find the derivative (which I know), but I can't find this until I have found the value of g(80).
b) Let h(v) be the gas consumption in L/h at velocity v. What is the relationship between h(v) and f(v)? Find h(80) and h`(80).
Okay, now I'm just lost. I don't even know where to start here.
c) How could you explain the practical meaning of the values of these function and their derivatives to a driver who knows no calculus?
I think I could get this on my own once I get help with the previous problems.