Question

The demand function, given the marginal demand D(x) = -1000/x^2, when the price is $4 per unit, is:

a) D(x) = -62.5
b) D(x) = -125
c) D(x) = -250
d) D(x) = -500

Answer 1

Integrating the given marginal demand function D(x) = -1000/x^2 and using the price of $4 per unit helps find the constant of the demand function, leading to the correct answer of D(x) = -250.

Step-by-step explanation:

The student's question revolves around finding the demand function given the marginal demand D(x) = -1000/x^2 and the price of $4 per unit. The first step is to integrate the marginal demand function to find the demand function. In this case, integration will give us D(x) = 1000/x + C, where C is the constant of integration. To find this constant, we use the information that the price is $4 per unit. Assuming that D(x) reflects the quantity demanded at the price x, and setting D(4) = 0 (because at the maximum price, the quantity demanded would be zero) we can solve for C.

Plugging the values into the demand function:

0 = 1000/4 + C

C = -250,

thus the demand function is D(x) = 1000/x - 250. The correct answer is c) D(x) = -250.