Suppose that the demand for a product depends on the price p according to , where p is in dollars. Find and explain the meaning of the instantaneous rate of change of demand with respect to price when .
A) -5.00. If price increases by $1, the demand will decrease approximately 5.00 units.
B) 5.00. If price increases by $1, the demand will increase approximately 5.00 units.
C) -10.00. If price increases by $1, the demand will decrease approximately 10.00 units.
D) -65.67. If price increases by $1, the demand will increase approximately 65.67 units.
E) 10.00. If price increases by $1, the demand will decrease approximately 10.00 units.

Question

Suppose that the demand for a product depends on the price p according to  , where p is in dollars. Find and explain the meaning of the instantaneous rate of change of demand with respect to price when  . ​
A) -5.00. If price increases by $1, the demand will decrease approximately 5.00 units. 
B) 5.00. If price increases by $1, the demand will increase approximately 5.00 units. 
C) -10.00. If price increases by $1, the demand will decrease approximately 10.00 units. 
D) -65.67. If price increases by $1, the demand will increase approximately 65.67 units. 
E) 10.00. If price increases by $1, the demand will decrease approximately 10.00 units.

Quizplus · Accepted Answer

The instantaneous rate of change of demand with respect to price is given by the derivative of the demand function with respect to price. 
Taking the derivative of Q(p)=1500-125p^2, we get dQ/dp= -250p.
When p = 6, dQ/dp= -250(6) = -1500.
This means that a $1 increase in price will lead to a decrease in demand by approximately 10 units, which is equal to the magnitude of the instantaneous rate of change of demand with respect to price. Therefore, choice C is correct.

Suppose That the Demand for a Product Depends on the Price