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? $

Question

Catherine

Mathematics

15 July, 17:06

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? $

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Lawson Walton · Answer 1

Below in bold.

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.