A company finds that the rate at which the quantity of a product that consumers demand changes with respect to price is given by the marginal-demand function Upper D prime (x )equals negative StartFraction 4000 Over x squared EndFraction where x is the price per unit, in dollars. Find the demand function if it is known that 1002 units of the product are demanded by consumers when the price is $4 per unit.

D(x) = 4000 / x + 2

Step-by-step explanation:

Given:

marginal-demand function = d /dx[D(x )] = D'(x)= -4000/x²

Quantity of product demanded = 1002 units

Price of product per unit = $4

To find:

demand function D(x)

Solution:

D'(x)= -4000/x²

      =  -4000/x² dx

      = -4000 x⁻² dx

D(x) = -4000 x⁻¹ + C

D(x) = -4000/x + C

Since we know that the quantity of product is 1002 and price per unit is $4 so,

D(4) = 1002 = 4000/4 + C

          1002 = 4000/4 + C  

          1002 = 1000 + C  

           1002 - 1000 = C

            C = 2

Hence the demand function is:

D(x) = 4000 / x + 2

(c, 0) i might be wrong so don't put full faith on my answer

step-by-step explanation: