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ive as a Rate of Change 121 19. Estimating the Values of a Function If /(100)- 5000 and T(100)-10, estimate each of the following. (a) (101) (b) f(100.5) (d) f(98) (c) f(99) (e) (99.75) 20. Estimating the Valu

ive as a Rate of Change 121 19. Estimating the Values of a Function If /(100)- 5000 and T(100)-10, estimate each of the following. (a) (101) (b) f(100.5) (d) f(98) (c) f(99) (e) (99.75) 20. Estimating the Valu

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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Readings Meter 43.2 #3.7 #4.2 -4.6 5.0 5.4 5.8 6.3 .8 -4 oving in a straight met (in seconds) is reference point, for when the time is ference point when object is 6 feet from A car is traveling between the two -rk during the next responding graph d. Id -t 1 (c) 1.8 The Derivative as a Rate of Change 121 19. Estimating the Values of a Function If /(100)- 5000 and T(100) 10, estimate each of the following. (a) (101) (c) f(99) (b) f(100.5) (d) f(98) (e) (99.75) 20. Estimating the Values of a Function If f(25)-10 and -2, estimate each of the following. f'(25) (a) (27) (c) (25.25) (e) (23.5) (b) (26) (d) (24) 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 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) 22 La nOA SI SIHL
Transcribed Image Text:Readings Meter 43.2 #3.7 #4.2 -4.6 5.0 5.4 5.8 6.3 .8 -4 oving in a straight met (in seconds) is reference point, for when the time is ference point when object is 6 feet from A car is traveling between the two -rk during the next responding graph d. Id -t 1 (c) 1.8 The Derivative as a Rate of Change 121 19. Estimating the Values of a Function If /(100)- 5000 and T(100) 10, estimate each of the following. (a) (101) (c) f(99) (b) f(100.5) (d) f(98) (e) (99.75) 20. Estimating the Values of a Function If f(25)-10 and -2, estimate each of the following. f'(25) (a) (27) (c) (25.25) (e) (23.5) (b) (26) (d) (24) 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 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) 22 La nOA SI SIHL
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