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's the maximum fuel economy of the car?

Answer 1

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Answer 2

Answer:

Maximum fuel economy is 25.572 miles per gallon.

Step-by-step explanation:

For the maximum fuel economy, we need to find the maximum value of the function f(s).

This is a quadratic with a negative leading coefficient, so it is a parabola that is open at the bottom, so its maximum value is at its vertex.

The vertex of a parabola ax² + bx + c occurs at x = -b/2a.

So for f(s), the maximum is at

s = -0.699 / ( 2 × -0.009 ) = 0.699 / 0.018 ≈ 38.833

The maximum value is then

f(38.833) ≈ 25.572