(a) Explanation Given: The function is, y = − 2 x 3 − 3 x 2 + 8 and the interval is [ − 2 , 6 ] . Formula used: Average rate of change: The average rate of change of f ( x ) with respect to x for a function f as x changes from a to b is, f ( b ) − f ( a ) b − a . Calculation: Substitute a = − 2 and b = 6 in f ( b ) − f ( a ) b − a and obtain the average rate of change as follows. f ( 6 ) − f ( − 2 ) 6 − ( − 2 ) (1) Compute the value of f ( − 2 ) as follows. f ( − 2 ) = − 2 ( − 2 ) 3 − 3 ( − 2 ) 2 + 8 = − 2 ( − 8 ) − 3 ( 4 ) + 8 = 16 − 12 + 8 = 12 Compute the value of f ( 6 ) as follows (b) To determine To estimate: The instantaneous rate of change at x = − 2 .

Calculus with Applications Books a la Carte Edition

11th Edition

ISBN: 9780133864564

Author: Margaret L. Lial; Nathan P. Ritchey; Raymond N. Greenwell

Publisher: Pearson Education

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Chapter 3, Problem 48RE

(a)

To determine

To find: The average rate of change for the function y=−2x3−3x2+8 over the interval [−2,6] .

(b)

To determine

To estimate: The instantaneous rate of change at x=−2 .

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Chapter 3, Problem 47RE

Chapter 3, Problem 49RE

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Calculus with Applications Books a la Carte Edition

Ch. 3.1 - YOUR TURN 1 Find . Ch. 3.1 - YOUR TURN 2 Find . Ch. 3.1 - Prob. 3YT Ch. 3.1 - YOUR TURN 4 Find . Ch. 3.1 - YOUR TURN 5 Find . Ch. 3.1 - YOUR TURN 6 Find . Ch. 3.1 - Prob. 7YT Ch. 3.1 - Prob. 8YT Ch. 3.1 - Prob. 1WE Ch. 3.1 - Prob. 2WE

Ch. 3.1 - Prob. 3WE Ch. 3.1 - Prob. 4WE Ch. 3.1 - In Exercises 1-4, choose the best answer for each...Ch. 3.1 - In Exercises 1-4, choose the best answer for each...Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Decide whether each limit exists. If a limit...Ch. 3.1 - Decide whether each limit exists. If a limit...Ch. 3.1 - Prob. 7E Ch. 3.1 - Decide whether each limit exists. If a limit...Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Decide whether each limit exists. If a limit...Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - 14. In Exercise 10, why does , even though f(1) =...Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Complete the tables and use the results to find...Ch. 3.1 - Complete the tables and use the results to find...Ch. 3.1 - Complete the tables and use the results to find...Ch. 3.1 - Prob. 21E Ch. 3.1 - Let and . Use the limit rules to find each...Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Let and . Use the limit rules to find each...Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 36E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 39E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 49E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 51E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - 56. Let Find Find Ch. 3.1 - 57. Does a value of k exist such that the...Ch. 3.1 - 58. Repeat the instructions of Exercise 57 for the...Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - Prob. 61E Ch. 3.1 - Prob. 62E Ch. 3.1 - Prob. 63E Ch. 3.1 - Prob. 64E Ch. 3.1 - Prob. 65E Ch. 3.1 - Prob. 66E Ch. 3.1 - Prob. 67E Ch. 3.1 - Prob. 68E Ch. 3.1 - Prob. 69E Ch. 3.1 - Prob. 70E Ch. 3.1 - Prob. 71E Ch. 3.1 - Prob. 72E Ch. 3.1 - Prob. 73E Ch. 3.1 - Find each of the following limits (a) by...Ch. 3.1 - Prob. 75E Ch. 3.1 - Prob. 76E Ch. 3.1 - Prob. 77E Ch. 3.1 - Prob. 78E Ch. 3.1 - Prob. 79E Ch. 3.1 - Prob. 80E Ch. 3.1 - Prob. 81E Ch. 3.1 - Prob. 82E Ch. 3.1 - Prob. 83E Ch. 3.1 - 84. APPLY IT Consumer Demand When the price of an...Ch. 3.1 - 85. Sales Tax Officials in California tend to...Ch. 3.1 - Prob. 86E Ch. 3.1 - 87. Average Cost The cost (in dollars) for...Ch. 3.1 - Prob. 88E Ch. 3.1 - Prob. 89E Ch. 3.1 - 90. Preferred Stock In business finance, an...Ch. 3.1 - Prob. 91E Ch. 3.1 - Prob. 92E Ch. 3.1 - 93. Sediment To develop strategies to manage water...Ch. 3.1 - Prob. 94E Ch. 3.1 - Prob. 95E Ch. 3.2 - YOUR TURN 1 Find all values x = a where the...Ch. 3.2 - YOUR TURN 2 Find all values of x where the...Ch. 3.2 - Find each of the following limits. W1. Ch. 3.2 - Prob. 2WE Ch. 3.2 - Prob. 3WE Ch. 3.2 - Prob. 4WE Ch. 3.2 - Prob. 5WE Ch. 3.2 - In Exercises 1–6, find all values x = a where the...Ch. 3.2 - In Exercises 1–6, find all values x = a where the...Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - In Exercises 1–6, find all values x = a where the...Ch. 3.2 - Prob. 6E Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Prob. 11E Ch. 3.2 - Prob. 12E Ch. 3.2 - Prob. 13E Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Find all values x = a where the function is...Ch. 3.2 - Prob. 19E Ch. 3.2 - In Exercises 19–24, (a) graph the given function,...Ch. 3.2 - In Exercises 19–24, (a) graph the given function,...Ch. 3.2 - In Exercises 19–24, (a) graph the given function,...Ch. 3.2 - Prob. 23E Ch. 3.2 - Prob. 24E Ch. 3.2 - Prob. 25E Ch. 3.2 - In Exercises 25–28, find the value of the constant...Ch. 3.2 - In Exercises 25–28, find the value of the constant...Ch. 3.2 - In Exercises 25–28, find the value of the constant...Ch. 3.2 - Prob. 29E Ch. 3.2 - Prob. 30E Ch. 3.2 - Prob. 31E Ch. 3.2 - Prob. 32E Ch. 3.2 - Prob. 33E Ch. 3.2 - Prob. 34E Ch. 3.2 - 35. Production The graph shows the profit from the...Ch. 3.2 - 36. Cost Analysis The cost to transport a mobile...Ch. 3.2 - Prob. 37E Ch. 3.2 - Prob. 38E Ch. 3.2 - Prob. 39E Ch. 3.2 - Prob. 40E Ch. 3.2 - Prob. 41E Ch. 3.3 - YOUR TURN 1 The projected U.S. Asian population...Ch. 3.3 - Prob. 2YT Ch. 3.3 - Prob. 3YT Ch. 3.3 - Prob. 4YT Ch. 3.3 - Prob. 5YT Ch. 3.3 - Prob. 1WE Ch. 3.3 - Prob. 2WE Ch. 3.3 - Prob. 3WE Ch. 3.3 - Prob. 4WE Ch. 3.3 - Prob. 1E Ch. 3.3 - Find the average rate of change for each function...Ch. 3.3 - Prob. 3E Ch. 3.3 - Prob. 4E Ch. 3.3 - Find the average rate of change for each function...Ch. 3.3 - Find the average rate of change for each function...Ch. 3.3 - Find the average rate of change for each function...Ch. 3.3 - Prob. 8E Ch. 3.3 - Prob. 9E Ch. 3.3 - Prob. 10E Ch. 3.3 - Prob. 11E Ch. 3.3 - Prob. 12E Ch. 3.3 - Prob. 13E Ch. 3.3 - Prob. 14E Ch. 3.3 - Find the instantaneous rate of change for each...Ch. 3.3 - Find the instantaneous rate of change for each...Ch. 3.3 - Prob. 17E Ch. 3.3 - Find the instantaneous rate of change for each...Ch. 3.3 - Prob. 19E Ch. 3.3 - Prob. 20E Ch. 3.3 - Prob. 21E Ch. 3.3 - Prob. 22E Ch. 3.3 - Prob. 23E Ch. 3.3 - Prob. 24E Ch. 3.3 - Prob. 25E Ch. 3.3 - 26. Revenue The revenue (in thousands of dollars)...Ch. 3.3 - Prob. 27E Ch. 3.3 - 28. Interest If $1000 is invested in an account...Ch. 3.3 - Prob. 29E Ch. 3.3 - Prob. 30E Ch. 3.3 - Prob. 31E Ch. 3.3 - Prob. 32E Ch. 3.3 - Prob. 33E Ch. 3.3 - Prob. 34E Ch. 3.3 - Prob. 35E Ch. 3.3 - Prob. 36E Ch. 3.3 - Prob. 37E Ch. 3.3 - Prob. 38E Ch. 3.3 - Prob. 39E Ch. 3.3 - Prob. 40E Ch. 3.3 - Prob. 41E Ch. 3.3 - Prob. 42E Ch. 3.3 - Prob. 43E Ch. 3.3 - Prob. 44E Ch. 3.4 - YOUR TURN 1 For the graph of f(x) = x2 − x, (a)...Ch. 3.4 - Prob. 2YT Ch. 3.4 - Prob. 3YT Ch. 3.4 - Prob. 4YT Ch. 3.4 - Prob. 5YT Ch. 3.4 - Prob. 6YT Ch. 3.4 - Prob. 7YT Ch. 3.4 - Find for each of the following...Ch. 3.4 - Prob. 2WE Ch. 3.4 - Prob. 3WE Ch. 3.4 - Prob. 4WE Ch. 3.4 - 1. By considering, but not calculating, the slope...Ch. 3.4 - Prob. 2E Ch. 3.4 - Prob. 3E Ch. 3.4 - Prob. 4E Ch. 3.4 - Prob. 5E Ch. 3.4 - Prob. 6E Ch. 3.4 - Prob. 7E Ch. 3.4 - Estimate the slope of the tangent line to each...Ch. 3.4 - Prob. 9E Ch. 3.4 - Prob. 10E Ch. 3.4 - Prob. 11E Ch. 3.4 - Using the definition of the derivative, find...Ch. 3.4 - Prob. 13E Ch. 3.4 - Prob. 14E Ch. 3.4 - Prob. 15E Ch. 3.4 - Prob. 16E Ch. 3.4 - Using the definition of the derivative, find...Ch. 3.4 - Using the definition of the derivative, find...Ch. 3.4 - Prob. 19E Ch. 3.4 - Using the definition of the derivative, find...Ch. 3.4 - Prob. 21E Ch. 3.4 - For each function, find (a) the equation of the...Ch. 3.4 - For each function, find (a) the equation of the...Ch. 3.4 - For each function, find (a) the equation of the...Ch. 3.4 - For each function, find (a) the equation of the...Ch. 3.4 - For each function, find (a) the equation of the...Ch. 3.4 - Prob. 27E Ch. 3.4 - Prob. 28E Ch. 3.4 - Prob. 29E Ch. 3.4 - Prob. 30E Ch. 3.4 - Prob. 31E Ch. 3.4 - Prob. 32E Ch. 3.4 - Prob. 33E Ch. 3.4 - Prob. 34E Ch. 3.4 - Find the x-values where the following do not have...Ch. 3.4 - Find the x-values where the following do not have...Ch. 3.4 - Prob. 37E Ch. 3.4 - Find the x-values where the following do not have...Ch. 3.4 - Prob. 39E Ch. 3.4 - In Exercises 40 and 41, tell which graph, (a) or...Ch. 3.4 - Prob. 41E Ch. 3.4 - Prob. 42E Ch. 3.4 - Prob. 43E Ch. 3.4 - Prob. 44E Ch. 3.4 - Prob. 45E Ch. 3.4 - Prob. 46E Ch. 3.4 - Prob. 47E Ch. 3.4 - Prob. 48E Ch. 3.4 - 49. Demand Suppose the demand for a certain item...Ch. 3.4 - Prob. 50E Ch. 3.4 - Prob. 51E Ch. 3.4 - 52. Cost The cost in dollars of producing x tacos...Ch. 3.4 - Prob. 54E Ch. 3.4 - Prob. 55E Ch. 3.4 - Prob. 56E Ch. 3.4 - Prob. 57E Ch. 3.4 - Prob. 58E Ch. 3.4 - Prob. 59E Ch. 3.4 - Prob. 60E Ch. 3.4 - Prob. 61E Ch. 3.5 - YOUR TURN 1 Sketch the graph of the derivative of...Ch. 3.5 - Prob. 2YT Ch. 3.5 - Prob. 1WE Ch. 3.5 - Prob. 2WE Ch. 3.5 - Prob. 1E Ch. 3.5 - Prob. 2E Ch. 3.5 - Prob. 3E Ch. 3.5 - Prob. 4E Ch. 3.5 - Prob. 5E Ch. 3.5 - Prob. 6E Ch. 3.5 - Prob. 7E Ch. 3.5 - Sketch the graph of the derivative for each...Ch. 3.5 - Sketch the graph of the derivative for each...Ch. 3.5 - Prob. 10E Ch. 3.5 - Prob. 11E Ch. 3.5 - Sketch the graph of the derivative for each...Ch. 3.5 - Prob. 13E Ch. 3.5 - Prob. 14E Ch. 3.5 - Prob. 15E Ch. 3.5 - Prob. 16E Ch. 3.5 - Business and Economics 17. Consumer Demand When...Ch. 3.5 - Prob. 18E Ch. 3.5 - Prob. 19E Ch. 3.5 - 20. Flight Speed The graph below shows the...Ch. 3.5 - Prob. 21E Ch. 3.5 - 22. Weight Gain The graph below shows the typical...Ch. 3.5 - Prob. 23E Ch. 3.5 - Prob. 24E Ch. 3 - Prob. 1RE Ch. 3 - Prob. 2RE Ch. 3 - Prob. 3RE Ch. 3 - Prob. 4RE Ch. 3 - Determine whether each of the following statements...Ch. 3 - Prob. 6RE Ch. 3 - Prob. 7RE Ch. 3 - Prob. 8RE Ch. 3 - Prob. 9RE Ch. 3 - Prob. 10RE Ch. 3 - Prob. 11RE Ch. 3 - Prob. 12RE Ch. 3 - Prob. 13RE Ch. 3 - Prob. 14RE Ch. 3 - Prob. 15RE Ch. 3 - Prob. 16RE Ch. 3 - Prob. 17RE Ch. 3 - Prob. 18RE Ch. 3 - Prob. 19RE Ch. 3 - Prob. 20RE Ch. 3 - Prob. 21RE Ch. 3 - Prob. 22RE Ch. 3 - Prob. 23RE Ch. 3 - Prob. 24RE Ch. 3 - Prob. 25RE Ch. 3 - Prob. 26RE Ch. 3 - Prob. 27RE Ch. 3 - Prob. 28RE Ch. 3 - Prob. 29RE Ch. 3 - Prob. 30RE Ch. 3 - Prob. 31RE Ch. 3 - Prob. 32RE Ch. 3 - Prob. 33RE Ch. 3 - Prob. 34RE Ch. 3 - Prob. 35RE Ch. 3 - Prob. 36RE Ch. 3 - Prob. 37RE Ch. 3 - Prob. 38RE Ch. 3 - Prob. 39RE Ch. 3 - Prob. 40RE Ch. 3 - Prob. 41RE Ch. 3 - Prob. 42RE Ch. 3 - Prob. 43RE Ch. 3 - Prob. 44RE Ch. 3 - Prob. 45RE Ch. 3 - Prob. 46RE Ch. 3 - Prob. 47RE Ch. 3 - Prob. 48RE Ch. 3 - Prob. 49RE Ch. 3 - Prob. 50RE Ch. 3 - Prob. 51RE Ch. 3 - Prob. 52RE Ch. 3 - Prob. 53RE Ch. 3 - Prob. 54RE Ch. 3 - Prob. 55RE Ch. 3 - Prob. 56RE Ch. 3 - Prob. 57RE Ch. 3 - Prob. 58RE Ch. 3 - Prob. 59RE Ch. 3 - Prob. 60RE Ch. 3 - Prob. 61RE Ch. 3 - Prob. 62RE Ch. 3 - Prob. 63RE Ch. 3 - Prob. 64RE Ch. 3 - Prob. 65RE Ch. 3 - Prob. 66RE Ch. 3 - Prob. 67RE Ch. 3 - Prob. 68RE Ch. 3 - Prob. 69RE Ch. 3 - Prob. 70RE Ch. 3 - Prob. 71RE Ch. 3 - Prob. 72RE Ch. 3 - Prob. 73RE

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The average rate of change for the function y = − 2 x 3 − 3 x 2 + 8 over the interval [ − 2 , 6 ] .