Word Problem

Question

The fuel efficiency for a particular car is given by f(x) = -0.018x² + 1.656x + 4.4. Where x is the speed of the car in miles per hour and f(x) is the fuel efficiency in miles per gallon (mpg). What speed will yield the maximum fuel efficiency?

Answer 1

Find f'(x) to determine the critical points. The maximum fuel efficiency will occur at one of the critical points. 

 

f'(x) = -0.036x + 1.656

 

The critical points will occur where f'(x) = 0

 

-0.036x + 1.656 = 0

-0.036x = -1.656

x = 46 is the critical number for this function

 

Now, evaluate f(46) to determine the maximum fuel efficiency