Computing the Limit of a Difference Quotient In this activity, you will compute the limit of a difference quotient to determine the rate of change of a function at different points along its curve. Part A Consider the function fo) =x-4r +2, Calculate the limit of the difference quotient at xp3 for fx). BIU X X,L Characters used: 0/15000 Part B Find the equation of a line passing through the same point that fx) passes through at x 3 with a slope equal to the limit you found in part A. BI X X

Computing the Limit of a Difference Quotient In this activity, you will compute the limit of a difference quotient to determine the rate of change of a function at different points along its curve. Part A Consider the function fo) =x-4r +2, Calculate the limit of the difference quotient at xp3 for fx). BIU X X,L Characters used: 0/15000 Part B Find the equation of a line passing through the same point that fx) passes through at x 3 with a slope equal to the limit you found in part A. BI X X

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.6: Optimization

Problem 11E: Maximum Sales Growth This is a continuation of Exercise 10. In this exercise, we determine how the...

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Maximum Sales Growth This is a continuation of Exercise 10. In this exercise, we determine how the sales level that gives the maximum growth rate is related to the limit on sales. Assume, as above, that the constant of proportionality is 0.3, but now suppose that sales grow to a level of 4 thousand dollars in the limit. a. Write an equation that shows the proportionality relation for G. b. On the basis of the equation from part a, make a graph of G as a function of s. c. At what sales level is the growth rate as large as possible? d. Replace the limit of 4 thousand dollars with another number, and find at what sales level the growth rate is as large as possible. What is the relationship between the limit and the sales level that gives the largest growth rate? Does this relationship change if the proportionality constant is changed? e. Use your answers in part d to explain how to determine the limit if we are given sales data showing the sales up to a point where the growth rate begins to decrease.
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