7. A landlord rents out apartments for $900 per unit and has all 50 rented. For every time he raises the price by $25 he loses one unit. Any rented units also cost $75 a month in repairs. Create a function to represent the ratio of revenue to cost. a) Analyze the function represented by the problem using the first and second derivatives to find local extrema points and points of inflection. b) Do interval tests with each derivative to find intervals of increase and decrease and intervals of concavity. c) If the function is rational, find any asymptotes. d) Sketch a graph of the function, the first derivative, and the second derivative on large paper (use different colours for each function).
7. A landlord rents out apartments for $900 per unit and has all 50 rented. For every time he raises the price by $25 he loses one unit. Any rented units also cost $75 a month in repairs. Create a function to represent the ratio of revenue to cost. a) Analyze the function represented by the problem using the first and second derivatives to find local extrema points and points of inflection. b) Do interval tests with each derivative to find intervals of increase and decrease and intervals of concavity. c) If the function is rational, find any asymptotes. d) Sketch a graph of the function, the first derivative, and the second derivative on large paper (use different colours for each function).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:7. A landlord rents out apartments for $900 per unit and has all 50 rented. For every time he raises the
price by $25 he loses one unit. Any rented units also cost $75 a month in repairs. Create a function to
represent the ratio of revenue to cost.
a) Analyze the function represented by the problem using the first and second derivatives to find
local extrema points and points of inflection.
b) Do interval tests with each derivative to find intervals of increase and decrease and intervals of
concavity.
c) If the function is rational, find any asymptotes.
d) Sketch a graph of the function, the first derivative, and the second derivative on large paper (use
different colours for each function).
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