Question

Suppose the demand for a certain item is given by:

​D(p) = - 5p^2-6p+400​, 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 ​$9.

Answer 1

a. D'(p) = -10p - 6

b. There is a decrease of 96 units of demand for each dollar increase

Explanation:

The demand function is:

`D(p) = - 5p^2-6p+400`

(a) The derivate of the demand function with respect to price gives us the rate of change of demand:

`(dD(p))/(dp)=D'(p) = -10p-6`

(b) When p = $9, the rate of change of demand is:

`D'(9) = -10*9-6\\D'(9) = -96\ (units)/(\$)`

This means that, when p = $9, there is a decrease of 96 units of demand for each dollar increase.