A car dealer determines that if gasoline-electric hybrid automobiles are sold for x dollars apiece and the price of gasoline is y cents per gallon, then approximately h hybrid cars will be sold each year, where


h(x,y)=3,500−19x^1/2+6(0.1y+16)^3/2


She estimates that t years from now, the hybrid cars will be selling for


x(t) = 35,050 + 350t


dollars apiece and that gasoline will cost


y(t)=300+10(3t)^1/2

cents per gallon. At what rate will the annual demand for the hybrid cars be changing with respect to time 3 years from now? Will it be increasing or decreasing?

Q&A Education