數學題1........

1. When the price of a certain commodity is p dollars per unit, the manufacturer is willing to supply x hundred units, where
3p^2-x^2=12
How fast is the quantity supplied changing with respect to time when the price is $4 per unit and the price is increasing at the rate of 87 cents ($0.87) per week with respect to time?
Answer
3p^2-x^2=12
d/dt (3p^2-x^2)=0
(6p)(dp/dt)-2x(dx/dt)=0...(*)
when p=4
3(4)^2-x^2=12
x=6
ALSO dp/dt=0.87
substitute this information into (*)
(6*4)(0.87)-2(6)(dx/dt)=0
20.88-12(dx/dt)=0
dx/dt=1.74
the quantity supplied changing is 1.74 hundred units with respect to time