Word Problem

Question

The fuel efficiency F for a particular car is given by F(x) = -0.018x² + 1.656 + 4.4. Where x is the speed of the car in miles per hour (mph) and F(x) is the core fuel efficiency in miles per gallon (mpg), what speed will yield the maximum fuel efficiency?

 

Note: Please assist with necessary multiples parts and/or equations involving a possible parabola, critical points, etc. to reach a solution. Thanks so much!!

Answer 1

F(x) = -0.018x^2 + 1.656x + 4.4;   I'm assuming that the middle term, 1.656, should read 1.656x

 

this is the equation of a parabola, F(x) = Ax^2 + Bx + C, with A = -0.018, B = 1.656, C = 4.4, opening downward (since A < 0), with

 

F(0) = 4.4

 

the coordinates of the vertex (H,K) of such a parabola are given by:   H = -B/(2A);  and K = F(H);  in this case, we are

 

not actually interested in K, but only in H, which is found to be H = -B/(2A) = -1.656/[2(-0.018)] = .... , which is the

 

speed making H(x) a maximum, i.e., we are at the vertex of the parabola.