Question

The fuel consumption (gallons per hour) of a car traveling at a speed of v miles per hour is c = f(v).

1) What is the meaning of the derivative f ' (v)?
answer: rate of change of fuel consumption as miles go up

2) What are its units?
answer: miles per gallon

3) Write a sentence that explains the meaning of the equation f ' (20) = -0.05
answer: for every 20 miles, the fuel consumption goes down by 0.05

are my answers correct?

Answer 1

#1 ok
#2 f' = dc/dv = (gal/hr)/(mi/hr) = gal/mile
#3 sort of - see units for #2.

Answer 2

so for #3 would it be for every 20 gallons, the amount of miles the car is able to travel goes down by 0.05?

Answer 3

No, at 20 mi/hr, every mi/hr increase in speed decreases the fuel consumption by .05 gal/hr.

Keep track of the units.

Seems kind of odd though, that rate of fuel consumption decreases with increasing speed...