Question

The number of portable CD players you are prepared to supply to a retail outlet every week is given by the formula:
q = 0.1p2 + 2p
where p is the price it offers you. The retail outlet is currently offering you $50 per CD player. If the price it offers decreases at a rate of $1 per week, how will this affect the number you supply?

Answer 1

q = 0.1p^2 + 2p
dq/dt = (0.2p + 2) dp/dt
at p=50,
dq/dp = (10+2)(-1) = -12

so the number supplied is decreasing by 12 per week.