An economist is interested in how the price of a certain item affects its sales. When the price of the item is $ p, the number of items sold will be q = f(p). (This is the idea of "demand") Suppose we found out that f(150) = 2,000 and that f'(150) = -25. (a) Sketch the information of two boldface statements in a quick picture/sketch: (b) Write out in words what the first statement f(150) = = 2,000 means in the context. (c) The fact that the derivative is negative reflects what natural phenomenon?
An economist is interested in how the price of a certain item affects its sales. When the price of the item is $ p, the number of items sold will be q = f(p). (This is the idea of "demand") Suppose we found out that f(150) = 2,000 and that f'(150) = -25. (a) Sketch the information of two boldface statements in a quick picture/sketch: (b) Write out in words what the first statement f(150) = = 2,000 means in the context. (c) The fact that the derivative is negative reflects what natural phenomenon?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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Transcribed Image Text:An economist is interested in how the price of a certain item affects its sales. When the price of
the item is $ p, the number of items sold will be q = f(p). (This is the idea of "demand")
Suppose we found out that f(150) = 2,000 and that f'(150) = -25.
(a) Sketch the information of two boldface
statements in a quick picture/sketch:
(b) Write out in words what the first statement f(150) = 2,000 means in the context.
(c) The fact that the derivative is negative reflects what natural phenomenon?
(d) Write out in words what the statement f'(150) = -25 means in the context.
(Add in appropriate units!)
(e) Use the information given to estimate f(151) and f(149.5).
Show your work, and explain your rationale for proceeding as you did.
A little picture would be ideal to explain your thinking.
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