Answered: The accounting team at a manufacturing…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

The accounting team at a manufacturing business developed a model for the company's profit over its first year of business. Their profit, in thousands of dollars, followed the graph of p(t)= (1/6)t³-t²+t where t is the number of months since January 1st.

Use the mean value theorem to find the month in which the profits changed at the same rate as the average rate of change during the first 7 months. Midnight on New Year’s Eve corresponds to t=0,so for purposes of the mean value theorem, the first six months of the year correspond to the interval [0, 7].

Hint: Discard any solutions that are not in the corresponding open interval.

Note: Use a calculator to determine the solution. Write your answer as the name of the month, not a number. For example, the value t=2.3 corresponds to some time in March, so you would say the answer is "March."

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