#1 ok
#2 f' = dc/dv = (gal/hr)/(mi/hr) = gal/mile
#3 sort of - see units for #2.
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?
3 answers
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?
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...
Keep track of the units.
Seems kind of odd though, that rate of fuel consumption decreases with increasing speed...