03_M_GOLD_9004_12_ch02-1 - Chapter 2 Applications of the...

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71 Chapter 2 Applications of the Derivative 2.1 Describing Graphs of Functions 1. (a), (e), (f) 2. (c), (d) 3. (b), (c), (d) 4. (a), (e) 5. Increasing for x < .5, relative maximum point at x = .5, maximum value = 1, decreasing for x > .5, concave down, y -intercept (0, 0), x -intercepts (0, 0) and (1, 0). 6. Increasing for x < –.4, relative maximum point at x = –.4, relative maximum value = 5.1, decreasing for x > –.4, concave down for x < 3, inflection point (3, 3), concave up for x > 3, y -intercept (0, 5), x -intercept (–3.5, 0). The graph approaches the x -axis as a horizontal asymptote. 7. Decreasing for x < 0, relative minimum point at x = 0, relative minimum value = 2, increasing for 0 < x < 2, relative maximum point at x = 2, relative maximum value = 4, decreasing for x > 2, concave up for x < 1, inflection point at (1, 3), concave down for x > 1, y -intercept at (0, 2), x -intercept (3.6, 0). 8. Increasing for x < –1, relative maximum at x = –1, relative maximum value = 5, decreasing for –1 < x 2.9, relative minimum at x = 2.9, relative minimum value = –2, increasing for x > 2.9, concave down for x < 1, inflection point at (1, .5), concave up for x > 1, y -intercept (0, 3.3), x -intercepts (–2.5, 0), (1.3, 0), and (4.4, 0). 9. Decreasing for x < 2, relative minimum at x = 2, minimum value = 3, increasing for x > 2, concave up for all x , no inflection point, defined for x > 0, the line y = x is an asymptote, the y -axis is an asymptote. 10. Increasing for all x , concave down for x < 3, inflection point at (3, 3), concave up for x > 3, y -intercept (0, 1), x -intercept (–.5, 0). 11. Decreasing for 1 x < 3, relative minimum at x = 3, relative minimum value = .9, increasing for x > 3, maximum value = 6 (at x = 1), minimum value = .9 (at x = 3), concave up for 1 x < 4, inflection point at (4, 1.5), concave down for x > 4, the line y = 4 is an asymptote. 12. Increasing for x < –1.5, relative maximum at x = –1.5, relative maximum value = 3.5, decreasing for –1.5 < x < 2, relative minimum at x = 2, relative minimum value = –1.6, increasing from –2 < x < 5.5, relative maximum at x = 5.5, relative maximum value = 3.4, decreasing for x > 5.5, concave down for x < 0, inflection point at (0, 1), concave up for 0 < x < 4, inflection point at (4, 1), concave down for x > 4, y -intercept (0, 1), x -intercepts (–2.8, 0), (.6, 0), (3.5, 0), and (6.7, 0). 13. Slope decreases for all x . 14. Slope decreases for x < 3, increases for x > 3. 15. Slope decreases for x < 1, increases for x > 1. Minimum slope occurs at x = 1. 16. Slope decreases for x < 3, increases for x > 3. 17. a. C, F b. A, B, F c. C 18. a. A, E b. D c. E 19. x y 20. x y 21. x y
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72 Chapter 2: Applications of the Derivative 22. x y 23. t y 24. 25. t y 5 4 3 2 1 noon 100 ° 101 ° 102 ° 104 ° 103 ° y = T ( t ) 26. t y y = f ( t ) 40 27. x y y = C ( x ) Cost 28. t y 10 1 .25 4 29. Oxygen content decreases until time a , at which time it reaches a minimum. After a , oxygen content steadily increases. The rate of increase increases until b , and then decreases. Time b is the time when oxygen content is increasing fastest. 30. 1975 31. 1960 32. 1999; 1985 33. The parachutist’s speed levels off to 15 ft/sec.
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03_M_GOLD_9004_12_ch02-1 - Chapter 2 Applications of the...

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