Demand Function for Desk Lamps The demand function for the Luminar desk lamp is given by p = f(x) = −0.1x2 − 0.2x + 20 where x is the quantity demanded in thousands and p is the unit price in dollars. (a) Find f '(x). f '(x) = Correct: Your answer is correct. (b) What is the rate of change of the unit price (in dollars per 1,000 lamps) when the quantity demanded is 11,000 units (x = 11)? $ per 1,000 lamps What is the unit price (in dollars) at that level of demand? $

a. Find f '(x). f '(x)

This means that we should find the marginal value if x and this will be:

f(x) = −0.1x² − 0.2x + 20  = -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 11,000 units?

= -0.2x - 0.2

= -0.2(11000/1000) - 0.2

= -2(11) - 0.2

= -2.2 -02.

= -2.4

The unit price will be:

p = -0.1x² − 0.2x + 20  

p = -0.1(11)² - 0.2(11) + 20

p = -12.1 - 2.2 + 20

p = $5.7

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Step-by-step explanation:

f(x) = -0.1x^2 - 0.2x + 20

(a) f'(x) = -0.2x - 0.2

(b)  When 11,000 units are demanded

Rate of change = f' (11) =  -0.2(11) - 0.2

= -2.4 dollars / 1000 lamps.

Unit price at this level of demand =  p

= -0.1(11)^2 - 0.2(11) + 20

= 5.7 dollars.

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