Your Porsche's gas mileage (in miles per gallon) is given as a function M(x) of speed x in miles per hour. It is found that
M'(x) =
3,600x−2 − 1
(3,600x−1 + x)2
.
Estimate M'(10), M'(60), and M'(110). (Round your answers to seven decimal places.)
M'(10) = 1 mpg/mph
M'(60) = 2 mpg/mph
M'(110) = 3 mpg/mph
What do the answers tell you about your car?
The results mean that at a speed of 10 mph, the fuel economy is increasing at a rate of 4 miles per gallon per 1-mph increase in speed, at a speed of 60 mph, the fuel economy is neither increasing nor decreasing, and at a speed of 110 mph, the fuel economy is decreasing at a rate of 5 miles per gallon per 1-mph increase in speed. Thus 60 mph is the most fuel-efficient speed for the car.
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