A car travels at a constant speed and burns g(x) litres of gas per kilometer, where x is the speed of the car in kilometers per hour and g(x) = 1280 + x^2/320x

Question

a) If gas costs $1.29 per litre, find the cost function C(x) that expresses the cost of the fuel for a 200 km trip as a function of the speed.

b) What driving speed will make the cost of fuel equal to $300?

c) Determine the driving speed that will minimize the total fuel cost for the trip.