Question

The fuel economy (in miles per gallon) of a certain car is e(x) = −0.01x2 0.64x 10.4, where x is the driving speed (in miles per hour, 20 ≤ x ≤ 60). at what speed is fuel economy greatest?

a) 20 mph
b) 35 mph
c) 45 mph
d) 60 mph

Answer 1

The speed at which fuel economy is greatest is 32 mph.

Step-by-step explanation:

To find the speed at which fuel economy is greatest, we need to find the maximum value of the function e(x) = -0.01x^2 + 0.64x + 10.4. This is a quadratic function in the form ax^2 + bx + c.

We know that for a quadratic function in the form ax^2 + bx + c, the x-coordinate of the vertex is given by -b / (2a). In this case, a = -0.01 and b = 0.64.

Using the formula, we find that the x-coordinate of the vertex is -0.64 / (2*(-0.01)) = 32.

Therefore, the speed at which fuel economy is greatest is 32 mph.