The demand function for the Luminar desk lamp is given by

Question

p = f(x) = −0.1x^2 − 0.7x + 20
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 3,000 units (x = 3)?

Answer 1

(a) differentiating ... f'(x) = -0.2 x - 0.7

(b) to find dp/dx , plug x=3 into f'(x)