Question

Most cars get their best gas mileage when traveling at a relatively modest speed. The gas mileage M for a certain new car is modeled by the function M(s) = 1∕28s² + 3s - 31 for 15 ≤ s ≤ 70

where s is the speed in mi/h and M is measured in mi/gal. What is the car's best gas mileage, and at what speed is it attained?

Answer 1

The car's best gas mileage is 3.5 mi/gal and it is attained at a speed of 84 mi/h.

Step-by-step explanation:

To find the car's best gas mileage and the speed at which it is attained, we need to find the vertex of the function M(s) = 1/28s² + 3s - 31. The vertex of a quadratic function in the form f(x) = ax² + bx + c is given by the formula x = -b/2a.

For the given function M(s) = 1/28s² + 3s - 31, a = 1/28 and b = 3. Plugging these values into the formula, we get s = -3 / (2 * (1/28)) = -84. Therefore, the speed at which the car's best gas mileage is attained is 84 mi/h.

To find the best gas mileage, we substitute the speed s = 84 into the function M(s). M(84) = 1/28(84)² + 3(84) - 31 = 3.5 mi/gal. Therefore, the car's best gas mileage is 3.5 mi/gal.