Question

Suppose the demand for a certain item is given by:

Answer 1

Answer:

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

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

Step-by-step 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:

$\frac{dD(p)}{dp}=D'(p) = -10p-6$

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

$D'(9) = -10*9-6\\D'(9) = -96\ \frac{units}{\ }$

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