The fuel efficiency F for a particular car is given by Fx 0

The fuel efficiency F for a particular car is given by F(x) = -0.018 x^2 + 1.548 x + 5.8 where x is the speed of the car in miles per hour (mph) and F(x) is the correspo efficiency in miles per gallon (mpg). (a) What is the fuel efficiency if the car\'s speed is 60 mph? (b) What speed will yield the maximum fuel efficiency? Show work.

Solution

F(x) = - 0.018x^2 + 1.548x + 5.8

x = speed in mph

a) Fuel efficiency when x= 60 mph

F(60) = -0.018(60)^2 + 1.548(60) + 5.8 = 33.88 mpg

b) max. efficiency would occur at vertex of quaratic function:

F(x) = - 0.018x^2 + 1.548x + 5.8

x = - (1.548/2*-0.018) = 43 mph

F(43) = - 0.018(43^2 + 1.548(43) + 5.8 = 39.082 mpg