Question
Asked Feb 5, 2020
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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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Expert Answer

Step 1

Given:

Demand function

Calculus homework question answer, step 1, image 1
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Step 2

For part (a)

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

Calculus homework question answer, step 2, image 1
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Step 3

For part (b)

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

Calculus homework question answer, step 3, image 1
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