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1.8 The Derivative as a Rate of Change 121 19. Estimating the Values of a Function If f(100)-5000 and T(100)-10, estimate each of the following. (a) (101) (b) f(100.5) (d) (98) (c) (99) (e) (99.75) 20. Estimating the Values of a Function If f(25)-10 and f'(25)-2, estimate each of the following. (a) f(27) (c) f(25.25) (e) (23.5) (b) (26) (d) (24)

1.8 The Derivative as a Rate of Change 121 19. Estimating the Values of a Function If f(100)-5000 and T(100)-10, estimate each of the following. (a) (101) (b) f(100.5) (d) (98) (c) (99) (e) (99.75) 20. Estimating the Values of a Function If f(25)-10 and f'(25)-2, estimate each of the following. (a) f(27) (c) f(25.25) (e) (23.5) (b) (26) (d) (24)

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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Q19&Q29 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
meter Readings Times Trip Meter 43.2 43.7 44.2 44.6 45.0 45.4 45.8 46.3 46.8 47.4 is moving in a straight on at timer (in seconds) is t of a reference point, for object when the time is the reference point when n the object is 6 feet from Graph A car is traveling artway between the two ew York during the next he corresponding graph y speed. 0 -t 1 vad tol (c) 1.8 The Derivative as a Rate of Change 121 19. Estimating the Values of a Function If f(100)- 5000 and 10, estimate each of the following. T(100) (a) (101) (b) f(100.5) (d) (98) (e) f(99) (e) f(99.75) 20. Estimating the Values of a Function If f(25)-10 and f'(25)-2, estimate each of the following. (a) f(27) (b) f(26) (d)/(24) (c) f(25.25) (e) (23.5) 21. Temperature of a Cup of Coffee Let f(t) be the temperature of a cup of coffee t minutes after it has been poured. Inter- pret f(4) 120 and f'(4)=-5. Estimate the temperature of the coffee after 4 minutes and 6 seconds, that is, after 4.1 minutes. 22. Rate of Elimination of a Drug Suppose that 5 mg of a drug is injected into the bloodstream. Let f(t) be the amount pres- ent in the bloodstream after r hours. Interpret f(3) = 2 and f(3) =-.5. Estimate the number of milligrams of the drug in the bloodstream after 3 hours. 23. Price Affects Sales Let f(p) be the number of cars sold when the price is p dollars per car. Interpret the statements (10,000) = 200,000 and f(10,000) = -3. 24. Advertising Affects Sales Let f(x) be the number of toys sold when x dollars are spent on advertising. Interpret the state- ments f(100,000) = 3,000,000 and (100,000) = 30. 25. Rate of Sales Let f(x) be the number (in thousands) of com- puters sold when the price is x hundred dollars per computer. Interpret the statements f(12) = 60 and f'(12) = -2. Then, estimate the number of computers sold if the price is set at $1250 per computer. 26. Marginal Cost Let C(x) be the cost (in dollars) of manufac- turing x items. Interpret the statements C(2000) = 50,000 and C(2000) 10. Estimate the cost of manufacturing 1998 items. 27. Marginal Profit Let P(x) be the profit (in dollars) from manu- facturing and selling x cars. Interpret P(100) = 90,000 and P'(100) 1200. Estimate the profit from manufacturing and selling 99 cars. 28. Price of a Company's Stock Let f(x) be the value in dollars of one share of a company x days since the company went public. (a) Interpret the statements f(100) = 16 and f'(100) = .25. (b) Estimate the value of one share on the 101st day since the company went public. 29. Marginal Cost Analysis Consider the cost function C(x) = 6x² + 14x + 18 (thousand dollars). (a) What is the marginal cost at production level .x = 5? (b) Estimate the cost of raising the production level from x = 5 to x = 5.25. (c) Let R(x)=x² + 37x + 38 denote the revenue in thou- sands of dollars generated from the production of x units. What is the breakeven point? (Recall that the breakeven point is when revenue is equal to cost.) (d) Compute and compare the marginal revenue and mar- ginal cost at the breakeven point. Should the company
Transcribed Image Text:meter Readings Times Trip Meter 43.2 43.7 44.2 44.6 45.0 45.4 45.8 46.3 46.8 47.4 is moving in a straight on at timer (in seconds) is t of a reference point, for object when the time is the reference point when n the object is 6 feet from Graph A car is traveling artway between the two ew York during the next he corresponding graph y speed. 0 -t 1 vad tol (c) 1.8 The Derivative as a Rate of Change 121 19. Estimating the Values of a Function If f(100)- 5000 and 10, estimate each of the following. T(100) (a) (101) (b) f(100.5) (d) (98) (e) f(99) (e) f(99.75) 20. Estimating the Values of a Function If f(25)-10 and f'(25)-2, estimate each of the following. (a) f(27) (b) f(26) (d)/(24) (c) f(25.25) (e) (23.5) 21. Temperature of a Cup of Coffee Let f(t) be the temperature of a cup of coffee t minutes after it has been poured. Inter- pret f(4) 120 and f'(4)=-5. Estimate the temperature of the coffee after 4 minutes and 6 seconds, that is, after 4.1 minutes. 22. Rate of Elimination of a Drug Suppose that 5 mg of a drug is injected into the bloodstream. Let f(t) be the amount pres- ent in the bloodstream after r hours. Interpret f(3) = 2 and f(3) =-.5. Estimate the number of milligrams of the drug in the bloodstream after 3 hours. 23. Price Affects Sales Let f(p) be the number of cars sold when the price is p dollars per car. Interpret the statements (10,000) = 200,000 and f(10,000) = -3. 24. Advertising Affects Sales Let f(x) be the number of toys sold when x dollars are spent on advertising. Interpret the state- ments f(100,000) = 3,000,000 and (100,000) = 30. 25. Rate of Sales Let f(x) be the number (in thousands) of com- puters sold when the price is x hundred dollars per computer. Interpret the statements f(12) = 60 and f'(12) = -2. Then, estimate the number of computers sold if the price is set at $1250 per computer. 26. Marginal Cost Let C(x) be the cost (in dollars) of manufac- turing x items. Interpret the statements C(2000) = 50,000 and C(2000) 10. Estimate the cost of manufacturing 1998 items. 27. Marginal Profit Let P(x) be the profit (in dollars) from manu- facturing and selling x cars. Interpret P(100) = 90,000 and P'(100) 1200. Estimate the profit from manufacturing and selling 99 cars. 28. Price of a Company's Stock Let f(x) be the value in dollars of one share of a company x days since the company went public. (a) Interpret the statements f(100) = 16 and f'(100) = .25. (b) Estimate the value of one share on the 101st day since the company went public. 29. Marginal Cost Analysis Consider the cost function C(x) = 6x² + 14x + 18 (thousand dollars). (a) What is the marginal cost at production level .x = 5? (b) Estimate the cost of raising the production level from x = 5 to x = 5.25. (c) Let R(x)=x² + 37x + 38 denote the revenue in thou- sands of dollars generated from the production of x units. What is the breakeven point? (Recall that the breakeven point is when revenue is equal to cost.) (d) Compute and compare the marginal revenue and mar- ginal cost at the breakeven point. Should the company
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