Suppose the demand for a certain item is given by D(p)=-4p^2+8p+8, where p represents the price of the item in dollars. Currently the price of the item is $19. Use marginal demand to estimate the change in demand when the price is increased by one dollar
To find the marginal demand, we need to find the derivative of the demand function with respect to price (p):
D'(p) = -8p + 8
To estimate the change in demand when the price is increased by one dollar, we plug in the current price into the derivative:
D'(19) = -8(19) + 8
= -152 + 8
= -144
Therefore, the marginal demand when the price is $19 is -144. This means that for every one dollar increase in price, the demand for the item is expected to decrease by approximately 144 units.