Demand: Women's Boots The rate of change of the unit price p (in dollars) of a certain brand of women's boots is given by

Question

p'(x) = − 225x/(16 + x²)^3/2

^where x is the quantity demanded daily in units of a hundred. Find the demand function for these boots if the quantity demanded daily is 300 pairs (x = 3) when the unit price is $45/pair.

p(x) =

Answer 1

P(x) = 225/(16+x^2)^(1/2) + C

P(3) = 45

Thus, 45 = 225/(16+3^2)^(1/2) + C

45 = 225/5 + C

45 = 45 + C

C = 0

P(x) = 225/(16+x^2)^(1/2)

This is price as a function of demand.

To give demand as a function of price,

16+D^2 = 225^2/P^2

D = (225^2/P^2 - 16)^(1/2)