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?
#1 ok
#2 f' = dc/dv = (gal/hr)/(mi/hr) = gal/mile
#3 sort of - see units for #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?
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...
Your answers are partially correct. Here are the corrected answers for each question:
1) The derivative f'(v) represents the rate of change of fuel consumption with respect to the speed or rate at which the fuel consumption is changing as the speed increases or decreases.
2) The units of f'(v) are gallons per mile.
3) The equation f'(20) = -0.05 means that when the car is traveling at a speed of 20 miles per hour, the fuel consumption decreases by 0.05 gallons per mile. So, for every additional mile the car travels at a speed of 20 miles per hour, the fuel consumption decreases by 0.05 gallons.
Note: It is worth mentioning that the units in question 2 may vary depending on the specific function c = f(v) and its units.