The highway mileage m in miles per gallon for a compact car is approximated by m(s) = -0.025s2 + 2.45s - 30, where s is the speed in miles per hour. What is the maximum mileage for this compact car to the nearest tenth of a mile per gallon?

Question

mertsj · Answer

This is a parabola that is concave downward since the coefficient of the s^2 term is negative.  We could complete the square to find the vertex but it is probably easier to use the fact that the x coordinate of the vertex is x=-b/2a and then plug that value in to find the y coordinate of the vertex.  So here we go:

mertsj · Answer

$$x=\frac{-2.45}{2(-.025)}= 49$$

mertsj · Answer

Now replace s in the original equation with 49 and that will be the y coordinate of the vertex.

mertsj · Answer

$$y=-.025(49)^{2}+2.45(49)-30=30.025$$

mertsj · Answer

Is that what you got?

mertsj · Answer

So the maximum mileage is 30.0