The fuel efficiency F for a particular car is given by Fx 00

The fuel efficiency F for a particular car is given by F(x)= -0.018 x^2 + 1.656 x + 4.4 where x is the speed of the car in miles per hour (mph) and F(x) is the corresponding fuel efficiency in miles per gallon (mpg). What is the fuel efficiency if the car\'s speed is 70 mph? What speed will yield the maximum fuel efficiency? Show work.

Solution

(a) given x=70mph

F(70) = -0.018*70^2 + 1.656*70 + 4.4 = 32.12 mpg

(b) fuel efficiency is maximum when

dF/dx= 0

-0.018*2x + 1.656 =0

1,656 = 0.036x

x = 1.656/0.036 = 46 mph