# math

posted by Beth

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

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.

## Similar Questions

1. ### Math

A small truck is to be driven 300 miles on a freeway at a constant speed of x miles per hour. Speed laws on the freeway require that a truck must be driven between 30 miles per hour and 70 miles per hour. assume that fuel cost \$3.50 …
2. ### Algebra Word Problems

when going more than 38 miles per hour the gas mileage of a certain car fits the model y=43.81 - 3.95x where x is the speed of the car in miles per hor and y is the miles per gallon of gas. Based on model what speed will the car average …
3. ### statistics

An auto maker estimates that the mean gas mileage of its sport utility vehicle is 20 miles per gallon. A random sample of 8 such vehicles had a mean of 18 per gallon and a standard deviation of 5 miles per gallon. At รก=0.05, can you …
4. ### Calculus

You are the owner of a delivery company with one truck. The trucks fuel economy is 1200/x miles per gallon when driving at x miles per hour (where 80 >= x <= 110). The price of fuel is \$1 per gallon. You pay the truck driver …
5. ### biology

Given the part of the molecule shown below, can the underlined atom participate in a hydrogen bond with an approriate bonding partner?
6. ### Calculus

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'(90). (Round your answers …
7. ### Calculus

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'(90). (Round your answers …
8. ### math

Their car gets 30 miles per gallon in gas mileage. They are traveling for seven hours at a rate of 55 miles per hour. Assuming no stops, how much gas will they need to complete their seven hour trip?
9. ### Algebra

The fuel efficiency for a certain midsize car is given by E(v) = −0.017v^ + 1.462v + 3.5 where E(v)is the fuel efficiency in miles per gallon for a car traveling v miles per hour. (a) What speed will yield the maximum fuel efficiency?
10. ### statistics

the mean gas mileage for a hybrid car is 56 miles per gallon suppose that the gasoline mileage is approximately normally distributed of 3.2 miles per gallon what is the probability that a randomly selected hybrid gets more than 62 …

More Similar Questions