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Calculus 1. Abby has developed an app that focuses on connecting potential renters with owners of unoccupied holiday houses. Her current monthly profit (in hundreds of dollars) for a hundred home owners is given by p(x) = 5+10(x - 1)²-(x - 1)4. Abby's technical skills are limited and she is not able to expand the capability of her app to handle more than 300 house owners per month. (a) Calculate the maximum profit that Abby is able to make each month. (b) Find the the points x ≥ 0 for which the second derivative of p(x) is 0. (c) Find the point of diminishing returns for Abby's profit function.

Calculus 1. Abby has developed an app that focuses on connecting potential renters with owners of unoccupied holiday houses. Her current monthly profit (in hundreds of dollars) for a hundred home owners is given by p(x) = 5+10(x - 1)²-(x - 1)4. Abby's technical skills are limited and she is not able to expand the capability of her app to handle more than 300 house owners per month. (a) Calculate the maximum profit that Abby is able to make each month. (b) Find the the points x ≥ 0 for which the second derivative of p(x) is 0. (c) Find the point of diminishing returns for Abby's profit function.

Advanced Engineering Mathematics
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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Calculus 1. Abby has developed an app that focuses on connecting potential renters with owners of unoccupied holiday houses. Her current monthly profit (in hundreds of dollars) for x hundred home owners is given by p(x) = 5+10(x - 1)²-(x-1)4. Abby's technical skills are limited and she is not able to expand the capability of her app to handle more than 300 house owners per month. (a) Calculate the maximum profit that Abby is able to make each month. (b) Find the the points x ≥ 0 for which the second derivative of p(x) is 0. (c) Find the point of diminishing returns for Abby's profit function.
Transcribed Image Text:Calculus 1. Abby has developed an app that focuses on connecting potential renters with owners of unoccupied holiday houses. Her current monthly profit (in hundreds of dollars) for x hundred home owners is given by p(x) = 5+10(x - 1)²-(x-1)4. Abby's technical skills are limited and she is not able to expand the capability of her app to handle more than 300 house owners per month. (a) Calculate the maximum profit that Abby is able to make each month. (b) Find the the points x ≥ 0 for which the second derivative of p(x) is 0. (c) Find the point of diminishing returns for Abby's profit function.
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