Finding an Equation of a Tangent Line In Exercis and 62, find equations of the two tangent lines to the grap Approximating a Deri evaluate f(2) and f(2.1) and f that pass through the indicated point. 62. f(x) = x2 61. f(x) = 4x- x2 67. f(x) = x(4 - x y у Using the Derivative 10 (2, 5) 8 6 4 alternative fe 3 45 6 78 4 derivative at 3+ wwwe 2 y 69. f(x) = x3 + 2x2 + 1, -6-4 -2 2 4 6 70. g(x) = x2 - x, c = 1 -X RI,-3) -4 5 1 2 3 71. g(x) = x, c = 0 f A 63. Graphical Reasoning Use a each function and its tangent lines at x = -1, x = x =1. Based on the results, determine whether the slane tangent lines to the graph of a fanction at different values always distinct. graphing utility to 73. f(x) = (x - 6)2/3, c x 75. h(x) = lx +7|, c = C 1 2 3 Determir 77-80, de are differentia (b) g(x) = (a) f(x) x TY f(x)(x + 4)2/3 a function how you HOW DO YOU SEE IT? The figuré shows the graph of g'. 64. function Explain +t always -6 -4 -2 4 2+ nmetric metric 79, f(r -6-4 ob 151

Finding an Equation of a Tangent Line In Exercis and 62, find equations of the two tangent lines to the grap Approximating a Deri evaluate f(2) and f(2.1) and f that pass through the indicated point. 62. f(x) = x2 61. f(x) = 4x- x2 67. f(x) = x(4 - x y у Using the Derivative 10 (2, 5) 8 6 4 alternative fe 3 45 6 78 4 derivative at 3+ wwwe 2 y 69. f(x) = x3 + 2x2 + 1, -6-4 -2 2 4 6 70. g(x) = x2 - x, c = 1 -X RI,-3) -4 5 1 2 3 71. g(x) = x, c = 0 f A 63. Graphical Reasoning Use a each function and its tangent lines at x = -1, x = x =1. Based on the results, determine whether the slane tangent lines to the graph of a fanction at different values always distinct. graphing utility to 73. f(x) = (x - 6)2/3, c x 75. h(x) = lx +7|, c = C 1 2 3 Determir 77-80, de are differentia (b) g(x) = (a) f(x) x TY f(x)(x + 4)2/3 a function how you HOW DO YOU SEE IT? The figuré shows the graph of g'. 64. function Explain +t always -6 -4 -2 4 2+ nmetric metric 79, f(r -6-4 ob 151

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Description: 61 Finding an Equation of a Tangent Line In Exercisand 62, find equations of the two tangent lines to the grapApproximating a Derievaluate f(2) and f(2.1) andf that pass through the indicated point.62. f(x) = x261. f(x) = 4x- x267. f(x) = x(4 - xyуUs

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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