College Allgebra

Question

The fuel efficiency for a certain midsize car is given by
E(v) = −0.015v2 + 1.320v + 3.4
where E(v) the fuel efficiency in miles per gallon for a car traveling v miles per hour.
(a) What speed will yield the maximum fuel efficiency? Round to the nearest mile per hour.

(b) What is the maximum fuel efficiency for this car? Round to the nearest mile per gallon.

Answer 1

Because this equation has the shape of an inverted (upside down) parabola, all we need to do is find the vertex of this parabola.  We could also use Calculus to determine this, but I feel that is outside the scope of College Algebra.  We can find the v value of the vertex by simply finding -b/(2a)  where the equation is in the form E(v) = av²+bv+c.  In this case we find that the speed that gives us the maximum fuel efficiency(vertex) is at -1.32/(2*-.015) = 44 miles per hour.  Now that we know the speed, we can simply plug it in to the original equation to get the maximum fuel efficiency, so E(44) = -.015(44)² + 1.32(44) + 3.4  = 32.44 Miles per gallon.