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CalculusQ&A LibraryThe 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?Question

Asked Feb 5, 2020

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The demand function for the Luminar desk lamp is given by

p = f(x) = −0.1x^{2} − 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?

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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