1. The demand function for the Luminar desk lamp is given by p = f ( x ) = 0.1 x

Question

1. The demand function for the Luminar desk lamp is given by

p = f(x) = 0.1x2 0.4x + 23

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

(a) Find f'(x).
f'(x) =

(b) What is the rate of change of the unit price when the quantity demanded is 11000 units (x = 11)?

$ per 1000 lamps

What is the unit price at that level of demand?
$

2. The demand for Sportsman 5 X 7 tents is given by the following function where p is measured in dollars and x is measured in units of a thousand. (Round your answers to three decimal places.)

p = f(x) = 0.1x2 x + 40

(a) Find the average rate of change in the unit price of a tent if the quantity demanded is between the following intervals.

(b) What is the rate of change of the unit price if the quantity demanded is 5500?
$  per 1000 tents

Explanation / Answer

1.p=f(x)=-0.1x2-0.4x+23

a. f'(x)= -0.1(2)x-0.4=-0.2x-0.4

b. f'(11)=-0.2(11)-0.4=-2.6

c. f(11)=-0.1(11)2-0.4(11)+23=6.5

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