Find the car's best gas mileage given the following information.... (description)

Question

Most cars get their best gas mileage when traveling at relatively low speeds. Suppose the gas mileage for a particular car is given by the equation:

 

M(s)=(-1/28)s^2+3s-31

 

where s is the speed in miles per hour with 15 ≤ s ≤ 70 and M is measured in miles per gallon.

 

A.) At what speed does the car attain its best gas mileage?

 

B.) What is the car's best gas mileage?

Answer 1

The function is a parabola and the maximum occurs at the vertex.

 

M(s) = (-1/28)s²+3s -31

 

Complete the square to put function in graph form

 

M(s) = (-1/28) (s² - 84s        ) -31

M(s) = (-1/28) (s2 - 84s + 42² ) -31 + 63

M(s) = (-1/28) (s - 42)² + 32

 

Best mileage is at 42mph and is 32mpg.