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

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.

$f(s) = - 0.009( {s}^{2} - \frac{233}{3} s) + 12$

$f(s) = - 0.009( {s}^{2} - \frac{233}{3} s + {( - \frac{233}{6}) }^{2} ) + 12 + - - 0.009 {( - \frac{233}{6}) }^{2}$
$f(s) = - 0.009 {( s- \frac{233}{6}) }^{2} + 12 + 13.57225$

$f(s) = - 0.009 {( s- \frac{233}{6}) }^{2} + 25.57225$
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

Answer 2

Answer:

Option C is the correct answer.

Step-by-step 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

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

Option C is the correct answer.