Question

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 5000 Over x squared EndFraction where x is the price per​ unit, in dollars. Find the demand function if it is known that 1006 units of the product are demanded by consumers when the price is ​$5 per unit.

Answer 1

q = 5000/x + 6

Explanation:

D´= dq/dx = - 5000/x²

dq = -( 5000/x²)*dx

Integrating on both sides of the equation we get:

q = -5000*∫ 1/x²) *dx

q = 5000/x + K in this equation x is the price per unit and q demanded quantity and K integration constant

If when 1006 units are demanded when the rice is 5 then

x = 5 and q = 1006

1006 = 5000/5 +K

1006 - 1000 = K

K = 6

Then the demand function is:

q = 5000/x + 6