Question

The demand for a certain portable USB battery charger is given by D(P) = -2p2 + 2p+2, where p represents the price 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) The rate of change of demand with respect to price is

Answer 1

The rate of change of demand with respect to price can be found by taking the derivative of the demand function. When the price is $10, the rate of change of demand is -38.

Step-by-step explanation:

To find the rate of change of demand with respect to price, we need to take the derivative of the demand function.

D(P) = -2p^2 + 2p + 2

First, find the derivative of -2p^2, which is -4p.

Next, find the derivative of 2p, which is 2.

Since the constant term does not affect the rate of change, it is omitted when taking the derivative.

Therefore, the rate of change of demand with respect to price is given by dD/dP = -4p + 2.

(b) To find the rate of change of demand when the price is $10, substitute p = 10 into the derivative.

dD/dP = -4p + 2

dD/dP = -4(10) + 2

dD/dP = -40 + 2

dD/dP = -38

Therefore, when the price is $10, the rate of change of demand is -38.