67. CONSUMER DEMAND An importer of Brazilian coffee estimates that local consumers will buy approximately \( D(p)=\frac{4,374}{p^{2}} \) pounds of the coffee per week when the price is \( p \) dollars per pound. It is also estimated that \( t \) weeks from now, the price of Brazilian coffee will be \( p(t)=0.02 t^{2}+0.1 t+6 \) dollars per pound.
a. At what rate will the demand for coffee be changing with respect to price when the price is \( \$ 9 \) ?
b. At what rate will the demand for coffee be changing with respect to time 10 weeks from now? Will the demand be increasing or decreasing at this time?
