Suppose the demand for a certain item is given by D (p) equalsnegative 3psquarednegative 4pplus200 , where p represents the price of the item in dollars. a. Find the rate of change of demand with respect to price. b. Find and interpret the rate of change of demand when the price is $10.

(a) dD/dp = - 6p - 4

(b) dD/dp = - 64

Since the rate of change of demand is less than 1, the demand for the item is inelastic.

Explanation:

(a) D (p) = - 3p^2 - 4p + 200

The rate of change of demand with respect to price is obtained by differentiating D with respect to p

dD/dp = - 6p - 4

(b) dD/dp = - 6p - 4

p = $10

dD/dp = - 6 (10) - 4 = - 60 - 4 = - 64

The rate of change of demand with respect to price is less than 1. This means that the demand for the item is inelastic. An inelastic demand is one in which there is little or no change in quantity demanded when price increases or wanes.