Question

a car travels at a constants speed and uses G(x) litres of gas per kilomotre, where x is the speed of the car in kilomotres oer hour and G(x)=(1280+x^2)/(320x)

a>if fuel costs 1.29 per litre, determine the cost function C(x)that expresses the cost of the fuel for a 200KM trip as a function of the speed.
b>what driving speed will make the cost of fuel equal to 300
c>what driving speed will minimize the cost of fuel for the trip?

Answer 1

G(x) = 4/x + x/320

(a) C(x) = cost for x km trip
$ = liters * $/liter
liters = L/km * km
C(x) = G(x) * 200 * 1.29
= 258*G(x)
= 258(4/x + x/320) = 1032/x + 258/320 * x

(b) 300 = 1032/x + 258/320 x
96000x = 330240 + 258x^2
x = 3.4 or 368.6 ???!!!??

(c) C' = -1032/x^2 + 0.80625
C' = 0 at x = 35.8 km/h

If my math is right, that's some weird numbers...