Question

Most cars get their best gas mileage when traveling at a relatively slow speed. The gas mileage M for a certain new car is modeled by the function
M(s)= -1/28s^2+3s-31

where s is the speed in mi/h and M is measured in mi/gal.

Answer 1

In this item, it is assumed that we are to determine the speed at which the car will have the best gas mileage. This can be done by deriving the equation and equating it to zero.

       M(s) = -1/28s² + 3s - 31

Deriving,
    dM(s) = (-1/28)(2s) + 3 = 0

                     s = 42

Hence, the speed at which the best mileage is achieved is mi/h.