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E2RevAns - Review Answers Exam 2 1 a-64 units/sec b-32...

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Review Answers– Exam 2 1. a) -64 units/sec b) -32 units/sec 2. -14 3. -18 cents/unit 4. 2.4 in/hr 5. a) f 0 ( x ) = x (10 - 3 x 2 ) 5 - x 2 ; HT at: x = 0 , ± q 10 3 ; y = 7 2 x - 3 2 b) f 0 ( x ) = 2(6 x - 2) 2 ( x + 4)(15 x + 34) ; HTL at x = - 4 , 1 3 , - 34 15 ; y = 7840 x - 6240 c) y 0 = 1 + 8 x 1 3 3 x 2 3 ; HTL at: x = - 1 512 ; y = 3 x + 2 6. a = 15 7. zero acceleration: t = 5 and t = 5 ; at rest: t = 0 and t = 5 8. a) y 0 = 6 + 6 x ( x 2 + 3) 3 2 HTL at: ( - 1 , - 4 ) b) y 0 = 16 x y 2 y - 1 HTL at: ( 0 , 0 ) and ( 0 , 1 ) c) y 0 = x ( x - 2 y ) ( x - y )( x + y ) ; HTL at: ( 0 , 1 ) and ( - 3 r 8 3 , - 3 r 1 3 ) 9. a) 12 (1 + 2 x ) 5 2 b) 4 - 3 x 2 x 3 c) y 00 = y 2 - ( x - 1) 2 y 3 10. Increasing on ( 0 , 4 ) ; Decreasing on ( -∞ , 0 ) , ( 4 , ) ; Relative max= 1 16 at 4 (HTL) 11. Rel min at - 1 (HTL); Rel max at 1 (HTL); note: there are five critical numbers, however (three vertical tangent lines, no cusps) 12. (a) only ( f 0 (0) = 0 ) 13. a) 1 . 5 C ; 41 . 5 C b) 2 bpm per C c) ± 0 . 6 bpm per hour 14. 0 . 24 m 3 ; 480 pounds 15. a) cost rising on ( 0 , 5 2 ) ( 20 , ) b) C ( x ) = 100000 x - 1 + 100 x - 30 x 2 + x 3 ; C 0 ( x ) = 3 x 2 - 60 x + 100 - 100000 x - 2 so C 0 (10) = - 1200 dollars per thousand books, or -1.2 dollars per book. When the production is 10000, producing another book will reduce the average cost of all books by about 1.2 dollars. c) dC = C 0 (30)(0 . 5) = 16500
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