To determine To calculate: The location of local extremum of given function f ( x ) = x 11 / 5 − x 6 / 5 + 1 and the value of the function at this extremum. Explanation Given: The function, f ( x ) = x 11 / 5 − x 6 / 5 + 1 . Formula used: According to the first derivative test, if c is the only critical number of the given function for an interval [ a , b ] such that a < c < b . Consider, f is differential for every value of x in the interval except at x = c . 1. For f ′ ( a ) > 0 and f ′ ( b ) < 0 , there will be a local maxima at c . 2. For f ′ ( a ) < 0 and f ′ ( b ) > 0 , there will be a local minima at c . 3. There will be no local extrema when f ′ ( a ) and f ′ ( b ) are either both positive or both negative Calculation: The given function is, f ( x ) = x 11 / 5 − x 6 / 5 + 1 Differentiate the given function with respect to x . f ′ ( x ) = 11 5 ( x 11 / 5 − 1 ) − 6 5 ( x 6 / 5 − 1 ) = 11 5 x 6 / 5 − 6 5 x 1 / 5 = x 1 / 5 ( 11 5 x − 6 5 ) To find the critical numbers, put f ′ ( x ) = 0 and solve. x 1 / 5 ( 11 5 x − 6 5 ) = 0 11 5 x − 6 5 = 0 11 5 x = 6 5 x = 6 11 Therefore, the critical numbers are x = 0 and x = 6 11 Use first derivative test separately on 0 and 6 11 to determine the local extrema of the given function. Consider an interval [ − 1 , 5 11 ] such that − 1 < 0 < 5 11 . Find the value of f ′ ( − 1 ) f ′ ( − 1 ) = ( − 1 ) 1 / 5 ( 11 5 ( − 1 ) − 6 5 ) = ( − 1 ) 1 / 5 ( − 11 5 − 6 5 ) = ( − 1 ) 1 / 5 ( − 17 5 ) Find the value of f ′ ( 5 11 )

Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

11th Edition

ISBN: 9780321931078

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 12.1, Problem 29E

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To calculate: The location of local extremum of given function f(x)=x11/5−x6/5+1 and the value of the function at this extremum.

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Chapter 12.1, Problem 28E

Chapter 12.1, Problem 30E

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Chapter 12 Solutions

Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

Ch. 12.1 - Checkpoint 1 For what values of x is the function...Ch. 12.1 - Checkpoint 2 Find all intervals on which is...Ch. 12.1 - Checkpoint 3 Identity the x-values of all points...Ch. 12.1 - Checkpoint 4 Find the critical numbers for each of...Ch. 12.1 - Prob. 5CP Ch. 12.1 - Prob. 6CP Ch. 12.1 - Prob. 7CP Ch. 12.1 - Prob. 8CP Ch. 12.1 - Checkpoint 9 If a sales function is given by...Ch. 12.1 - Prob. 1E

Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E Ch. 12.1 - Prob. 9E Ch. 12.1 - Prob. 10E Ch. 12.1 - Prob. 11E Ch. 12.1 - Find the intervals on which each function is...Ch. 12.1 - Find the intervals on which each function is...Ch. 12.1 - Find the intervals on which each function is...Ch. 12.1 - Prob. 15E Ch. 12.1 - Prob. 16E Ch. 12.1 - Prob. 17E Ch. 12.1 - Prob. 18E Ch. 12.1 - Prob. 19E Ch. 12.1 - Prob. 20E Ch. 12.1 - Prob. 21E Ch. 12.1 - Determine the location of each local extremum of...Ch. 12.1 - Prob. 23E Ch. 12.1 - Prob. 24E Ch. 12.1 - Prob. 25E Ch. 12.1 - Prob. 26E Ch. 12.1 - Determine the location of each local extremum of...Ch. 12.1 - Determine the location of each local extremum of...Ch. 12.1 - In Exercises 29–40, use the first-derivative test...Ch. 12.1 - In Exercises 29–40, use the first-derivative test...Ch. 12.1 - In Exercises 29–40, use the first-derivative test...Ch. 12.1 - In Exercises 29–40, use the first-derivative test...Ch. 12.1 - In Exercises 29–40, use the first-derivative test...Ch. 12.1 - In Exercises 29–40, use the first-derivative test...Ch. 12.1 - In Exercises 29–40, use the first-derivative test...Ch. 12.1 - Prob. 36E Ch. 12.1 - Prob. 37E Ch. 12.1 - Prob. 38E Ch. 12.1 - Prob. 39E Ch. 12.1 - Prob. 40E Ch. 12.1 - Use the maximum/minimum finder on a graphing...Ch. 12.1 - Prob. 42E Ch. 12.1 - Prob. 43E Ch. 12.1 - Prob. 44E Ch. 12.1 - Prob. 45E Ch. 12.1 - 46. Business Operating profits (in billions of...Ch. 12.1 - Prob. 47E Ch. 12.1 - Prob. 48E Ch. 12.1 - Prob. 49E Ch. 12.1 - Prob. 50E Ch. 12.1 - 51. Physical Science A Boston Red Sox pitcher...Ch. 12.1 - 52. Business Revenue (in billions of dollars) from...Ch. 12.1 - 53. Social Science According to projections by the...Ch. 12.1 - 54. Business The number of full-time employees (in...Ch. 12.1 - Work these exercises. You may need to use the...Ch. 12.1 - 56. Business The number of common stock holders...Ch. 12.1 - 57. Natural Science The microbe concentration...Ch. 12.1 - Prob. 58E Ch. 12.1 - Prob. 59E Ch. 12.1 - Prob. 60E Ch. 12.1 - Prob. 61E Ch. 12.1 - Prob. 62E Ch. 12.1 - Prob. 63E Ch. 12.1 - Prob. 64E Ch. 12.1 - 65. Social Science A group of researchers found...Ch. 12.1 - Prob. 66E Ch. 12.1 - Prob. 67E Ch. 12.1 - Prob. 68E Ch. 12.1 - Prob. 69E Ch. 12.1 - Prob. 70E Ch. 12.2 - Prob. 1CP Ch. 12.2 - Prob. 2CP Ch. 12.2 - Prob. 3CP Ch. 12.2 - Prob. 4CP Ch. 12.2 - Prob. 5CP Ch. 12.2 - Prob. 6CP Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - In Exercises 19 and 20, P(t) is the price of a...Ch. 12.2 - In Exercise 19 and 20, is the price of a certain...Ch. 12.2 - Physical Science Each of the functions in...Ch. 12.2 - Physical Science Each of the functions in...Ch. 12.2 - Prob. 23E Ch. 12.2 - Prob. 24E Ch. 12.2 - Prob. 25E Ch. 12.2 - Prob. 26E Ch. 12.2 - Find the largest open intervals on which each...Ch. 12.2 - Prob. 28E Ch. 12.2 - Find the largest open intervals on which each...Ch. 12.2 - Find the largest open intervals on which each...Ch. 12.2 - Find the largest open intervals on which each...Ch. 12.2 - Find the largest open intervals on which each...Ch. 12.2 - Business In Exercises 33–36, find the point of...Ch. 12.2 - Business In Exercises 33–36, find the point of...Ch. 12.2 - Business In Exercises 33–36, find the point of...Ch. 12.2 - Business In Exercises 33–36, find the point of...Ch. 12.2 - Find all critical numbers of the functions in...Ch. 12.2 - Find all critical numbers of the functions in...Ch. 12.2 - Find all critical numbers of the functions in...Ch. 12.2 - Prob. 40E Ch. 12.2 - Prob. 41E Ch. 12.2 - Prob. 42E Ch. 12.2 - Prob. 43E Ch. 12.2 - Prob. 44E Ch. 12.2 - Prob. 45E Ch. 12.2 - Find all critical numbers of the functions in...Ch. 12.2 - Prob. 47E Ch. 12.2 - Prob. 48E Ch. 12.2 - Prob. 49E Ch. 12.2 - Prob. 50E Ch. 12.2 - Prob. 51E Ch. 12.2 - Prob. 52E Ch. 12.2 - Prob. 53E Ch. 12.2 - Prob. 54E Ch. 12.2 - Prob. 55E Ch. 12.2 - Prob. 56E Ch. 12.2 - Prob. 57E Ch. 12.2 - Prob. 58E Ch. 12.2 - Prob. 59E Ch. 12.2 - Prob. 60E Ch. 12.2 - Prob. 61E Ch. 12.2 - Prob. 62E Ch. 12.2 - Prob. 63E Ch. 12.2 - 64. Business The price of Starbucks Corporation...Ch. 12.2 - 65. Social Science The population of Wyoming (in...Ch. 12.2 - Prob. 66E Ch. 12.2 - Prob. 67E Ch. 12.2 - Prob. 68E Ch. 12.2 - Prob. 69E Ch. 12.3 - Checkpoint 1 Find the location of the absolute...Ch. 12.3 - Prob. 2CP Ch. 12.3 - Prob. 3CP Ch. 12.3 - Prob. 4CP Ch. 12.3 - Prob. 5CP Ch. 12.3 - Checkpoint 6 In Example 9, suppose annual demand...Ch. 12.3 - Find the location of the absolute maximum and...Ch. 12.3 - Find the location of the absolute maximum and...Ch. 12.3 - Find the location of the absolute maximum and...Ch. 12.3 - Find the location of the absolute maximum and...Ch. 12.3 - Find the location of the absolute maximum and...Ch. 12.3 - Find the location of the absolute maximum and...Ch. 12.3 - Find the absolute extrema of each function on the...Ch. 12.3 - Find the absolute extrema of each function on the...Ch. 12.3 - Find the absolute extrema of each function on the...Ch. 12.3 - Find the absolute extrema of each function on the...Ch. 12.3 - Prob. 11E Ch. 12.3 - Find the absolute extrema of each function on the...Ch. 12.3 - Find the absolute extrema of each function on the...Ch. 12.3 - Find the absolute extrema of each function on the...Ch. 12.3 - Find the absolute extrema of each function on the...Ch. 12.3 - Prob. 16E Ch. 12.3 - Prob. 17E Ch. 12.3 - Prob. 18E Ch. 12.3 - Prob. 19E Ch. 12.3 - If possible, find an absolute extremum of each...Ch. 12.3 - If possible, find an absolute extremum of each...Ch. 12.3 - If possible, find an absolute extremum of each...Ch. 12.3 - If possible, find an absolute extremum of each...Ch. 12.3 - Prob. 24E Ch. 12.3 - Work these problems. (See Example 5.) 25. Business...Ch. 12.3 - Work these problems. (See Example 5.) 26. Business...Ch. 12.3 - 27. Business The number of employees of...Ch. 12.3 - 28. Social Science The number of people in...Ch. 12.3 - 29. Business Revenue generated by admissions to...Ch. 12.3 - 30. Health The number of heart transplants can be...Ch. 12.3 - 31. Business A manufacturer produces gas grills...Ch. 12.3 - 32. Business Saltwater taffy can be sold wholesale...Ch. 12.3 - 33. Natural Science A lake polluted by bacteria is...Ch. 12.3 - 34. Social Science The number of people in...Ch. 12.3 - 35. Health A disease has hit College Station,...Ch. 12.3 - Prob. 36E Ch. 12.3 - Prob. 37E Ch. 12.3 - Prob. 38E Ch. 12.3 - Prob. 39E Ch. 12.3 - Prob. 40E Ch. 12.3 - Prob. 41E Ch. 12.3 - 42. Business A cylindrical can of volume 58 cubic...Ch. 12.3 - Prob. 43E Ch. 12.3 - Prob. 44E Ch. 12.3 - Prob. 45E Ch. 12.3 - 46. Business A rectangular field is to be enclosed...Ch. 12.3 - 47. Business A mathematics book is to contain 36...Ch. 12.3 - Prob. 48E Ch. 12.3 - 49. Business If the price charged for a candy bar...Ch. 12.3 - 50. Business A company makes plastic buckets for...Ch. 12.3 - 51. Business We can use the function to model the...Ch. 12.3 - 52. Business A rock-and-roll band travels from...Ch. 12.3 - 53. Natural Science Homing pigeons avoid flying...Ch. 12.3 - 54. Business A company wishes to run a utility...Ch. 12.3 - Prob. 55E Ch. 12.3 - Prob. 56E Ch. 12.3 - Prob. 57E Ch. 12.3 - Prob. 58E Ch. 12.3 - Prob. 59E Ch. 12.3 - 60. Business A restaurant has an annual demand for...Ch. 12.3 - 61. Business Choose the correct answer:* The...Ch. 12.4 - Checkpoint 1 Find for Ch. 12.4 - Prob. 2CP Ch. 12.4 - Prob. 3CP Ch. 12.4 - Prob. 4CP Ch. 12.4 - Prob. 5CP Ch. 12.4 - Prob. 6CP Ch. 12.4 - Checkpoint 7 Suppose the sales function in Example...Ch. 12.4 - Prob. 1E Ch. 12.4 - Prob. 2E Ch. 12.4 - Find by implicit differentiation. (See Examples...Ch. 12.4 - Find by implicit differentiation. (See Examples...Ch. 12.4 - Prob. 5E Ch. 12.4 - Prob. 6E Ch. 12.4 - Prob. 7E Ch. 12.4 - Prob. 8E Ch. 12.4 - Prob. 9E Ch. 12.4 - Prob. 10E Ch. 12.4 - Prob. 11E Ch. 12.4 - Find by implicit differentiation. (See Examples...Ch. 12.4 - Prob. 13E Ch. 12.4 - Prob. 14E Ch. 12.4 - Prob. 15E Ch. 12.4 - Find by implicit differentiation. (See Examples...Ch. 12.4 - Prob. 17E Ch. 12.4 - Prob. 18E Ch. 12.4 - Prob. 19E Ch. 12.4 - Find at the given point. (See Example 5.) 20. Ch. 12.4 - Find at the given point. (See Example 5.) 21. Ch. 12.4 - Prob. 22E Ch. 12.4 - Prob. 23E Ch. 12.4 - Find at the given point. (See Example 5.) 23. Ch. 12.4 - Prob. 25E Ch. 12.4 - Prob. 26E Ch. 12.4 - Prob. 27E Ch. 12.4 - Prob. 28E Ch. 12.4 - Prob. 29E Ch. 12.4 - Prob. 30E Ch. 12.4 - Prob. 31E Ch. 12.4 - Prob. 32E Ch. 12.4 - Find the equation of the tangent line to the curve...Ch. 12.4 - Prob. 34E Ch. 12.4 - Prob. 35E Ch. 12.4 - Prob. 36E Ch. 12.4 - Prob. 37E Ch. 12.4 - Prob. 38E Ch. 12.4 - Prob. 39E Ch. 12.4 - Prob. 40E Ch. 12.4 - 41. Business A night club has approximated the...Ch. 12.4 - 42. Business The demand to download a hit single...Ch. 12.4 - Prob. 43E Ch. 12.4 - 44. Business For the equation given in the...Ch. 12.4 - 45. Business For PepsiCo, Inc., the relationship...Ch. 12.4 - Prob. 46E Ch. 12.4 - Prob. 47E Ch. 12.4 - 48. Business At a certain online printing service,...Ch. 12.5 - Checkpoint 1 Given that R3 = 25n4, find when n =...Ch. 12.5 - Prob. 2CP Ch. 12.5 - Prob. 3CP Ch. 12.5 - Prob. 4CP Ch. 12.5 - Prob. 5CP Ch. 12.5 - Prob. 6CP Ch. 12.5 - Prob. 7CP Ch. 12.5 - Given that x and y are functions of time, find the...Ch. 12.5 - Given that x and y are functions of time, find the...Ch. 12.5 - Given that x and y are functions of time, find the...Ch. 12.5 - Given that x and y are functions of time, find the...Ch. 12.5 - Prob. 5E Ch. 12.5 - Prob. 6E Ch. 12.5 - Prob. 7E Ch. 12.5 - Prob. 8E Ch. 12.5 - Prob. 9E Ch. 12.5 - Given that x and y are functions of time, find the...Ch. 12.5 - Work these exercises. (See Examples 1, 3, and...Ch. 12.5 - Work these exercises. (See Examples 1, 3, and...Ch. 12.5 - Work these exercises. (See Examples 1, 3, and...Ch. 12.5 - Work these exercises. (See Examples 1, 3, and...Ch. 12.5 - Work these exercises. (See Examples 1, 3, and...Ch. 12.5 - Work these exercises. (See Examples 1, 3, and...Ch. 12.5 - Prob. 17E Ch. 12.5 - Prob. 18E Ch. 12.5 - Prob. 19E Ch. 12.5 - Work these exercises. (See Examples 1, 3, and...Ch. 12.5 - 21. Business An architectural firm must decide on...Ch. 12.5 - 22. Social Science During a six-game hitless slump...Ch. 12.5 - Work these exercises. (See Example...Ch. 12.5 - Work these exercises. (See Example...Ch. 12.5 - Work these exercises. (See Example...Ch. 12.5 - Work these exercises. (See Example...Ch. 12.5 - Work these exercises. 27. Business The campus...Ch. 12.5 - Work these exercises. 28. Business Following a...Ch. 12.5 - 29. Business During a local political race, the...Ch. 12.5 - Prob. 30E Ch. 12.5 - Prob. 31E Ch. 12.5 - Prob. 32E Ch. 12.6 - Prob. 1CP Ch. 12.6 - Prob. 2CP Ch. 12.6 - Prob. 3CP Ch. 12.6 - Prob. 4CP Ch. 12.6 - Prob. 1E Ch. 12.6 - Sketch the graph of the function. Identify any...Ch. 12.6 - Prob. 3E Ch. 12.6 - Prob. 4E Ch. 12.6 - Sketch the graph of the function. Identify any...Ch. 12.6 - Prob. 6E Ch. 12.6 - Sketch the graph of the function. Identify any...Ch. 12.6 - Prob. 8E Ch. 12.6 - Prob. 9E Ch. 12.6 - Prob. 10E Ch. 12.6 - Prob. 11E Ch. 12.6 - Sketch the graph of the function. Identify any...Ch. 12.6 - Prob. 13E Ch. 12.6 - Prob. 14E Ch. 12.6 - Prob. 15E Ch. 12.6 - Prob. 16E Ch. 12.6 - Prob. 17E Ch. 12.6 - Sketch the graph of the function. Identify any...Ch. 12.6 - Prob. 19E Ch. 12.6 - Prob. 20E Ch. 12.6 - Prob. 21E Ch. 12.6 - Prob. 22E Ch. 12.6 - Prob. 23E Ch. 12.6 - In Exercises 23–28, sketch the graph of a function...Ch. 12.6 - Prob. 25E Ch. 12.6 - In Exercises 23–28, sketch the graph of a function...Ch. 12.6 - In Exercises 23–28, sketch the graph of a function...Ch. 12.6 - In Exercises 23–28, sketch the graph of a function...Ch. 12.6 - 29. Business The accompanying figure shows the...Ch. 12.6 - 30. Refer to the graph in Exercise 29. Which...Ch. 12.6 - 31. Business The revenue function (in millions of...Ch. 12.6 - 32. Business The cost function (in millions of...Ch. 12.6 - 33. Social Science The percent of the population...Ch. 12.6 - 34. Health The percent of female graduates in...Ch. 12.6 - Use a graphing calculator or computer to find the...Ch. 12.6 - Use a graphing calculator or computer to find the...Ch. 12.6 - Use a graphing calculator or computer to find the...Ch. 12.6 - Use a graphing calculator or computer to find the...Ch. 12.6 - 39. Business The revenue (in billions of dollars)...Ch. 12.6 - 40. Business The revenue (in billions of dollars)...Ch. 12.6 - Use a graphing calculator or computer to find the...Ch. 12.6 - Prob. 42E Ch. 12.6 - Prob. 43E Ch. 12.6 - Prob. 44E Ch. 12 - Prob. 1CE Ch. 12 - Prob. 2CE Ch. 12 - Prob. 3CE Ch. 12 - Prob. 4CE Ch. 12 - Prob. 5CE Ch. 12 - 6. What is the optimum time interval between...Ch. 12 - A pharmaceutical company is planning to gradually...Ch. 12 - Prob. 1RE Ch. 12 - Prob. 2RE Ch. 12 - Prob. 3RE Ch. 12 - Prob. 4RE Ch. 12 - Prob. 5RE Ch. 12 - Prob. 6RE Ch. 12 - Prob. 7RE Ch. 12 - Prob. 8RE Ch. 12 - Prob. 9RE Ch. 12 - Prob. 10RE Ch. 12 - Prob. 11RE Ch. 12 - Prob. 12RE Ch. 12 - Prob. 13RE Ch. 12 - Prob. 14RE Ch. 12 - Prob. 15RE Ch. 12 - Prob. 16RE Ch. 12 - Prob. 17RE Ch. 12 - Prob. 18RE Ch. 12 - Prob. 19RE Ch. 12 - Prob. 20RE Ch. 12 - Prob. 21RE Ch. 12 - Prob. 22RE Ch. 12 - Prob. 23RE Ch. 12 - Prob. 24RE Ch. 12 - Prob. 25RE Ch. 12 - Prob. 26RE Ch. 12 - Prob. 27RE Ch. 12 - Prob. 28RE Ch. 12 - Prob. 29RE Ch. 12 - Prob. 30RE Ch. 12 - Prob. 31RE Ch. 12 - Prob. 32RE Ch. 12 - Prob. 33RE Ch. 12 - Prob. 34RE Ch. 12 - Prob. 35RE Ch. 12 - Prob. 36RE Ch. 12 - Prob. 37RE Ch. 12 - Prob. 38RE Ch. 12 - Prob. 39RE Ch. 12 - Prob. 40RE Ch. 12 - Prob. 41RE Ch. 12 - Prob. 42RE Ch. 12 - Prob. 43RE Ch. 12 - Prob. 44RE Ch. 12 - Prob. 45RE Ch. 12 - Prob. 46RE Ch. 12 - Prob. 47RE Ch. 12 - Prob. 48RE Ch. 12 - Prob. 49RE Ch. 12 - Prob. 50RE Ch. 12 - Prob. 51RE Ch. 12 - Prob. 52RE Ch. 12 - Prob. 53RE Ch. 12 - Prob. 54RE Ch. 12 - Prob. 55RE Ch. 12 - Prob. 56RE Ch. 12 - Prob. 57RE Ch. 12 - Prob. 58RE Ch. 12 - 59. Business A landscaper needs to design an...Ch. 12 - Prob. 60RE Ch. 12 - Prob. 61RE Ch. 12 - Prob. 62RE Ch. 12 - Prob. 63RE Ch. 12 - 64. Business How many phones need to be produced...Ch. 12 - Prob. 65RE Ch. 12 - Prob. 66RE Ch. 12 - Prob. 67RE Ch. 12 - Prob. 68RE Ch. 12 - Prob. 69RE Ch. 12 - Prob. 70RE Ch. 12 - Prob. 71RE Ch. 12 - Prob. 72RE Ch. 12 - Prob. 73RE Ch. 12 - 74. Social Science A baseball player hits the ball...

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