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Third Derivative The third derivative of a function f(x) is the derivative of the second derivative f"(x) and is denoted by f"(x). Compute f"(x) for the following functions: (a) f(x)=x5-x² + 3x (b) f(x) = 4x5/2 Compute

Third Derivative The third derivative of a function f(x) is the derivative of the second derivative f"(x) and is denoted by f"(x). Compute f"(x) for the following functions: (a) f(x)=x5-x² + 3x (b) f(x) = 4x5/2 Compute

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q37,Q39&Q49 needed Needed to be solved correctly in 30 minutes and get the thumbs up please show neat and clean work for it By hand solution needed for all three questions
(a) (b) dx² dy² dz (37. Manufacturing Cost Let C(x) be the cost (in dollars) of man- ufacturing x bicycles per day in a certain factory. Interpret C(50) 5000 and C'(50) = 45. 38. Estimate the cost of manufacturing 51 bicycles per day in Exercise 37. 39. A Revenue Function The revenue from producing (and selling) x units of a product is given by R(x) = 3x - .01x² dollars. (a) Find the marginal revenue at a production level of 20. (b) Find the production levels where the revenue is $200. 40. Profit and Marginal Profit Let P(x) be the profit from produc- ing (and selling) x units of goods. Match each question with the proper solution. Questions A. What is the profit from producing 1000 units of goods? B. At what level of production will the marginal profit be 1000 dollars? Example 5 corrected their projections and are now expecting the total sales for the x day of January to be thousand dollars. T(x) = 24 5 + 36 5(3x + 1)² (a) Let S(x) be as in Example 5. Compute 7(1), 7(1), S(1), and S'(1). (b) Compare and interpret the data in part (a) as they pertain to the sales on January 1. 47. Sales of Computers (a) Let A(x) denote the number (in hundreds) of comput- ers sold when x thousand dollars is spent on advertising. Represent the following statement by equations involving A or A': When $8000 is spent on advertising, the number of computers sold is 1200 and is rising at the rate of 50 computers for each $1000 spent on advertising. (b) Estimate the number of computers that will be sold if $9000 is spent on advertising.
Transcribed Image Text:(a) (b) dx² dy² dz (37. Manufacturing Cost Let C(x) be the cost (in dollars) of man- ufacturing x bicycles per day in a certain factory. Interpret C(50) 5000 and C'(50) = 45. 38. Estimate the cost of manufacturing 51 bicycles per day in Exercise 37. 39. A Revenue Function The revenue from producing (and selling) x units of a product is given by R(x) = 3x - .01x² dollars. (a) Find the marginal revenue at a production level of 20. (b) Find the production levels where the revenue is $200. 40. Profit and Marginal Profit Let P(x) be the profit from produc- ing (and selling) x units of goods. Match each question with the proper solution. Questions A. What is the profit from producing 1000 units of goods? B. At what level of production will the marginal profit be 1000 dollars? Example 5 corrected their projections and are now expecting the total sales for the x day of January to be thousand dollars. T(x) = 24 5 + 36 5(3x + 1)² (a) Let S(x) be as in Example 5. Compute 7(1), 7(1), S(1), and S'(1). (b) Compare and interpret the data in part (a) as they pertain to the sales on January 1. 47. Sales of Computers (a) Let A(x) denote the number (in hundreds) of comput- ers sold when x thousand dollars is spent on advertising. Represent the following statement by equations involving A or A': When $8000 is spent on advertising, the number of computers sold is 1200 and is rising at the rate of 50 computers for each $1000 spent on advertising. (b) Estimate the number of computers that will be sold if $9000 is spent on advertising.
112 CHAPTER 1 The Derivative 48. Estimating Sales of Toys A toy company introduces a new video game on the market. Let S(x) denote the number of 000 videos sold on the day, x, since the item was introduced. Let n be a positive integer. Interpret S(n), S'(n), and S(n) + S'(n). 49. Third Derivative The third derivative of a function f(x) is the derivative of the second derivative f"(x) and is denoted by f"(x). Compute f"(x) for the following functions: (a) f(x)=x5-x² + 3x (b) f(x) = 4x5/2 50 Computo the thind
Transcribed Image Text:112 CHAPTER 1 The Derivative 48. Estimating Sales of Toys A toy company introduces a new video game on the market. Let S(x) denote the number of 000 videos sold on the day, x, since the item was introduced. Let n be a positive integer. Interpret S(n), S'(n), and S(n) + S'(n). 49. Third Derivative The third derivative of a function f(x) is the derivative of the second derivative f"(x) and is denoted by f"(x). Compute f"(x) for the following functions: (a) f(x)=x5-x² + 3x (b) f(x) = 4x5/2 50 Computo the thind
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