Posted by **Beth** on Wednesday, March 9, 2011 at 12:31am.

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.

Need Help? Read It Watch It Chat About It

## Answer this Question

## Related Questions

Calculus - Your Porsche's gas mileage (in miles per gallon) is given as a ...

Calculus - Your Porsche's gas mileage (in miles per gallon) is given as a ...

Algebra Word Problems - when going more than 38 miles per hour the gas mileage ...

biology - Given the part of the molecule shown below, can the underlined atom ...

statistics - An auto maker estimates that the mean gas mileage of its sport ...

Math - A small truck is to be driven 300 miles on a freeway at a constant speed ...

math - Their car gets 30 miles per gallon in gas mileage. They are traveling ...

Algebra - The fuel efficiency for a certain midsize car is given by E(v) = &#...

algera - The fuel efficiency for a certain midsize car is given by E(v) = −...

Math/ Calculus Please HELP!!! - A truck driver, on assignment from the owner of ...