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The predicted sales revenue of the ABC Company, in tens of millions of dollars, is given by f (x) = 0.02x³ – 0.18x2 + 0.45x + 30.5, where x is in years, 0 < x5 6. Annual costs are given by the function c(x) = 0.15x + 10.5. Compute and analyze the profit function P(x). Find all critical numbers of P(x) and use a sign map of the first derivative to identify the relative maxima and minima. Use a sign map of the second derivative to locate all inflection points. Use this information to graph P(x). In your own words, interpret the positive inflection point.

The predicted sales revenue of the ABC Company, in tens of millions of dollars, is given by f (x) = 0.02x³ – 0.18x2 + 0.45x + 30.5, where x is in years, 0 < x5 6. Annual costs are given by the function c(x) = 0.15x + 10.5. Compute and analyze the profit function P(x). Find all critical numbers of P(x) and use a sign map of the first derivative to identify the relative maxima and minima. Use a sign map of the second derivative to locate all inflection points. Use this information to graph P(x). In your own words, interpret the positive inflection point.

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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The predicted sales revenue of the ABC Company, in tens of millions of dollars, is given by f (x) = 0.02x3 – 0.18x2 + 0.45x + 30.5 , where x is in years, 0 sxS 6. Annual costs are given by the function c(x) = 0.15x + 10.5. Compute and analyze the profit function P(x). Find all critical numbers of P(x) and use a sign map of the first derivative to identify the relative maxima and minima. Use a sign map of the second derivative to locate all inflection points. Use this information to graph P(x). In your own words, interpret the positive inflection point.
Transcribed Image Text:The predicted sales revenue of the ABC Company, in tens of millions of dollars, is given by f (x) = 0.02x3 – 0.18x2 + 0.45x + 30.5 , where x is in years, 0 sxS 6. Annual costs are given by the function c(x) = 0.15x + 10.5. Compute and analyze the profit function P(x). Find all critical numbers of P(x) and use a sign map of the first derivative to identify the relative maxima and minima. Use a sign map of the second derivative to locate all inflection points. Use this information to graph P(x). In your own words, interpret the positive inflection point.
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