Question

The fuel economy of a car, measured in miles per gallon, is modeled by the function ƒ(s) = –0.009s2 + 0.699s + 12 where s represents the average speed of the car, measured in miles per hour. What average speed results in the maximum fuel economy?

A. 25.57 miles per hour
B. −38.83 miles per hour
C. 38.83 miles per hour
D. 3.88 miles per hour

Answer 1

Option C is the correct answer.

Explanation:

The fuel economy of the car f(s) = –0.009s² + 0.699s + 12

We need to find average speed results in the maximum fuel economy.

At maximum efficiency derivative of f(s) is zero.

That is f'(s) = 0

`f'(s)=0\\\\ -0.009* 2s + 0.699=0\\\\0.018s=0.699\\\\s=38.33mph`

Option C is the correct answer.

Answer 2

ANSWER

C. 38.83 miles per hour.

EXPLANATION

It was given that, the fuel economy of a car, measured in miles per gallon, is modeled by the function


`f(s) = - 0.009 {s}^(2) + 0.699s + 12`

We rewrite the function in the vertex form by completing the square.


`f(s) = - 0.009( {s}^(2) - (233)/(3) s) + 12`


`f(s) = - 0.009( {s}^(2) - (233)/(3) s + {( - (233)/(6)) }^(2) ) + 12 + - - 0.009 {( - (233)/(6)) }^(2)`

`f(s) = - 0.009 {( s- (233)/(6)) }^(2) + 12 + 13.57225`


`f(s) = - 0.009 {( s- (233)/(6)) }^(2) + 25.57225`
Or


`f(s) = - 0.009 {( s- 38.83) }^(2) +25.57`

The vertex of this function is


`V(38.83,25.57)`

Hence the maximum fuel economy is 25.57 gallons and this occurred at an average speed of 38.83.

The correct answer is C