Answer:
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
