1. The demand q for a product at price p is given by
q = 10,000 - 50 √0.02p2 + 500
Find the rate of change of demand with respect to price.
2. The number of units x of a product that is supplied at price p is given by
x = √p - 1, p ≥ 1
If the price p is $10, what is the rate of change of the supply with respect to the price, and what does it tell us?