derivatives

[flyfsh4trt]

Here is the problem:

let f(v) be the gas consumption (in liters/km) of a car going at velocity v (in km/hr). In other words, f(v) tells you how many liters of gas the car uses to go one km, if it is going at velocity v. You are told that

f(80)=.05 and f'(80)=.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).

b) let h(v) be the gas consumption in liters per hour. In other words, h(v) tells you how many liteers of gas the car uses in one hour if it is going at velocity v. What is the relationship between h(v) and f(v)? Find h(80) and h'(80).

any help on this matter is much appreciated!

 

[Unco]

Firstly, I think we are to assume f(v) is of the form f(v) = av + b (a, b are constants). You can use f(80)=0.05 and f'(80)=0.0005 to solve for a and b.


In terms of units, f accepts km/hr and spits out L/km. Consider the same for g and h, and the relationships follow.