ODDREV03 - Review Exercises for Chapter 3 v02 sin 2 32 2200...

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Review Exercises for Chapter 3 43. changes from < 4961 feet 5 s 2200 d 2 16 cos 1 20 p 180 21 180 2 < 4961 feet D r < dr d u 5 s 11 2 10 d 180 5 10 1 180 2 dr 5 s 2200 d 2 16 s cos 2 d d 10 8 to 11 8 v 0 5 2200 ft y sec r 5 v 0 2 32 s sin 2 d 45. Let Using a calculator: ! 99.4 < 9.96995 < ! 100 1 1 2 ! 100 s 2 0.6 d 5 9.97 f s x 1D x d 5 ! 99.4 5 ! x 1 1 2 ! x dx f s x x d < f s x d 1 f 9 s x d dx f s x d 5 ! x , x 5 100, dx 52 0.6. 47. Let Using a calculator, 4 ! 624 < 4.9980. 5 5 2 1 500 5 4.998 f s x x d 5 4 ! 624 < 4 ! 625 1 1 4 s 4 ! 625 d 3 s 2 1 d f s x x d < f s x d 1 f s x d dx 5 4 ! x 1 1 4 4 ! x 3 dx f s x d 5 4 ! x , x 5 625, dx 1. 49. Let Then ! 4.02 < ! 4 1 1 2 ! 4 s 0.02 d 5 2 1 1 4 s 0.02 d . f s 4.02 d < f s 4 d 1 f s 4 d dx f s x d 5 1 y s 2 ! x d . f s x d 5 ! x , x 5 4, dx 5 0.02, 51. In general, when approaches D y . D x 0, dy 53. True 55. True Review Exercises for Chapter 3 163 1. A number c in the domain of f is a critical number if or is undefined at c . x 4 4 3 2 1 4 4 3 1 2 3 fc () = 0 ( ) is undefined. y f f s c d 5 0 3. Critical numbers: Left endpoint: Critical number: Critical number: Minimum Right endpoint: Maximum s 2 , 17.57 d s 2.73, 0.88 d s 0.41, 5.41 d s 0, 5 d x < 0.41, x < 2.73 5 0 when sin x 5 2 5 . g s x d 5 2 2 5 sin x 1 (2.73, 0.88) (6.28, 17.57) 18 4 2 g s x d 5 2 x 1 5 cos x , f 0, 2 ±
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164 Chapter 3 Applications of Differentiation 7. (a) f s 1 d 5 f s 7 d 5 0 x 21 0 46 2 4 6 2 6 4 y f s x d 5 3 2 | x 2 4 | (b) f is not differentiable at x 5 4. 13. c 5 x 1 1 x 2 2 5 Midpoint of f x 1 , x 2 ± 2 Ac 5 A s x 1 1 x 2 d f 9 s c d 5 2 Ac 1 B 5 A s x 1 1 x 2 d 1 B 5 A s x 1 1 x 2 d 1 B f s x 2 d 2 f s x 1 d x 2 2 x 1 5 A s x 2 2 2 x 1 2 d 1 B s x 2 2 x 1 d x 2 2 x 1 f s x d 5 2 Ax 1 B f s x d 5 Ax 2 1 Bx 1 C 15. Critical numbers: and x 5 7 3 x 5 1 5 s x 2 1 ds 3 x 2 7 d f s x d 5 s x 2 1 d 2 s 1 d 1 s x 2 3 ds 2 ds x 2 1 d f s x d 5 s x 2 1 d 2 s x 2 3 d Interval: Sign of Conclusion: Increasing Decreasing Increasing f s x d > 0 f s x d < 0 f s x d > 0 f s x d : 7 3 < x < ± 1 < x < 7 3 2 ± < x < 1 9. c 5 1 14 9 2 3 5 2744 729 < 3.764 f s c d 5 2 3 c 2 1 y 3 5 3 7 f s b d 2 f s a d b 2 a 5 4 2 1 8 2 1 5 3 7 f s x d 5 2 3 x 2 1 y 3 f s x d 5 x 2 y 3 , 1 x 8 11. c 5 0 f s c d 5 1 1 sin c 5 1 f s b d 2 f s a d b 2 a 5 s p y 2 d 2 s 2 y 2 d s y 2 d 2 s 2 y 2 d 5 1 f s x d 5 1 1 sin x f s x d 5 x 2 cos x , 2 2 x 2 17. Domain: Critical number: x 5 1 5 3 2 x 2 1 y 2 s x 2 1 d 5 3 s x 2 1 d 2 ! x h s x d 5 3 2 x 1 y 2 2 3 2 x 2 1 y 2 s 0, ± d h s x d 5 ! x s x 2 3 d 5 x 3 y 2 2 3 x 1 y 2 Interval: Sign of Conclusion: Decreasing Increasing h s x d > 0 h s x d < 0 h s x d : 1 < x < ± 0 < x < 1 5. Yes. f is continuous on differentiable on for satisfies f s c d 2 0. c 5 1 3 x 5 1 3 . f s x d 5 s x 1 3 ds 3 x 2 1 d 5 0 s 2 3, 2 d . f 2 3, 2 ± , f s 2 3 d 5 f s 2 d 5 0.
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Review Exercises for Chapter 3 165 19. Relative minimum: s 2, 2 12 d h 9 s t d 5 t 3 2 8 5 0 when t 5 2. h s t d 5 1 4 t 4 2 8 t Test Interval: Sign of Conclusion: Decreasing Increasing h s t d > 0 h s t d < 0 h s t d : 2 < t < ± 2 ± < t < 2 21.
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This note was uploaded on 05/18/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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ODDREV03 - Review Exercises for Chapter 3 v02 sin 2 32 2200...

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