Your Porsche\'s gas mileage (in miles per gallon) is given as a function M ( x )

Question

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'(50), M'(60), and M'(100). (Round your answers to seven decimal places.)

What do the answers tell you about your car?

The results mean that at a speed of 50 mph, the fuel economy is increasing at a rate of ___ 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 100 mph, the fuel economy is decreasing at a rate of ____ miles per gallon per 1-mph increase in speed. Thus 60 mph is the most fuel-efficient speed for the car.

Explanation / Answer

M'(50) = 1.4399328

M'(60) = 0.9999306

M'(100) = 0.3599459

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