The demand function for the Luminar desk lamp is given by p = f(x) = −0.1x^2 − 0.2x + 22

Question

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

(a) Find f'(x).

(b) What is the rate of change of the unit price (in dollars per 1,000 lamps) when the quantity demanded is 12,000 units (x = 12)?

Answer 1

f(x) = −0.1x^2 − 0.2x + 22

df/dx = f'(x) = -0.2x - 0.2

f ' (x) = -0.2 ( 12000 ) - 0.2 = -2 (12000)/10 - 0.2

= -24000/10 - 0.2

= -2400 - 0.2

= -2400.2