The demand function for the Luminar desk lamp is given byp = f(x) = −0.1x2 − 0.3x + 32where 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 4,000 units (x = 4)?$   per 1,000 lampsWhat is the unit price (in dollars) at that level of demand?

Question
Asked Oct 3, 2019
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The demand function for the Luminar desk lamp is given by
p = f(x) = −0.1x2 − 0.3x + 32
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 4,000 units (x = 4)?
$   per 1,000 lamps
What is the unit price (in dollars) at that level of demand?
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Expert Answer

Step 1

Consider the given demand function for the Luminar desk lamp,

f (x)-0.1x2-0.3x+32
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f (x)-0.1x2-0.3x+32

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Step 2

f(x)0.1(2x)-0.3(1)+0
=-0.2x-0.3
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f(x)0.1(2x)-0.3(1)+0 =-0.2x-0.3

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Step 3

...
f(x)0.2(4)-0.3
- 0.3
-0.8 0.3
=-1.1
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f(x)0.2(4)-0.3 - 0.3 -0.8 0.3 =-1.1

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Calculus

Derivative

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