A dealer in French wine calculates that local customers will purchase approximatelyD(p)=p24374

bottles of the wine per week when the price is p dollars per bottle. It is also projected that t weeks from now, the price of French wine will bep(t)=0.02t2+0.1t+6 dollars per bottle.

a. What will be the rate of change in demand for wine with respect to the price when the price is $9 per bottle?

b. What will be the rate of change in demand for wine with respect to time 10 weeks from now? Will the demand be on the rise or fall at this time?