What is the unit price (in dollars) at that level of demand?

Question

The demand function for the Luminar desk lamp is given by

p = f(x) = −0.1x² − 0.2x + 24

where x is the quantity demanded in thousands and p is the unit price in dollars.

(a)

Find f '(x).

f '(x) =  

−0.2x−0.2

 

 

(b)

What is the rate of change of the unit price (in dollars per 1,000 lamps) when the quantity demanded is 4,000 units (x = 4)?

$ -1.00 per 1,000 lamps

Answer 1

The answers seem to be given in the question itself, and they are correct. The derivative of the price function gives the marginal price as a function of demand. The marginal price at 4000 lamps can be found by calculating the marginal price function at x=4.