# The demand function for the Luminar desk lamp is given by p = f(x) = −0.1x2 − 0.5x + 22 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 7,000 units (x = 7)? What is the unit price (in dollars) at that level of demand?

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The demand function for the Luminar desk lamp is given by

p = f(x) = −0.1x2 − 0.5x + 22

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 7,000 units (x = 7)?

What is the unit price (in dollars) at that level of demand?
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Step 1

Given:

Demand function

Step 2

For part (a)

Differentiate w.r.t x to equation (1)

Step 3

For part (b)

The rate of change of unit price (in dollars per 1000 lamps...

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