Second hourly - Name MATH 151 Second Hourly-Spring 2013...

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Unformatted text preview: Name MATH 151 Second Hourly--Spring 2013 Instructor: Dr. A. Silverstein 3/13/13 Instructions: Show all work on the test paper. Put your name on the test paper and all scratch sheets. Decimal answers are permitted unless stated otherwise; show the values accurate to 4 places. The total points possible on this test are @. GOOD LUCK” ~ 1. For f(:c) = (2:1: + 4)(5:1: — 3) find the derivative both ways and show the answers are equivalent: a) Byalgebra flag )2 to x V , Q X, 4— 20 x ’12, a /0>< €o F’Kx22aox;+/I-/ ”"’+l‘lx»éz, b) By Product Rule M’w‘vic = 1(0’96‘3) r 572wa 7* lé’fl’évf—Zflx P 2’0 (10) 2. Find an equation of the tangent line to the curve :1 {,‘L O ,4, 4. l «,6- = 0.2553 — 5:132 + 2 - at m : — 1. Simplify your answer. ~ 2.. :: mf zf/zyé-j: ‘6’.)4 -1034, @flW} My (10) c7 914:)(‘14‘ é: é/ .2 ,2,[‘./) 3., {Xvi/2342, :4 $2 9944 [a4 .,, 7- a, 2, ef-fL pnf-o M27. 1 ,3,‘7_,r-«—3,L my”: -3,L,¢0,éj (42w r3Lz—4m6+e $40.6 +/0,é 7.44 ab yzzaéx+2¥ 4. For f (as) = 1:2 — 316 + 5, find f’ (2) using the definition of the derivative. Show all detail. Use the Power Rule as a check only. You may break up the steps as follows: 21) Find f (2 + h) and simplify your answer. 7&(L—PLV): (L‘fA)L’3(Z/‘7LA)+( ch+Lt)(z+L7) ”(a 9A #f T. ¢+y2+ae~¢ ~3Z+j (4) '—' 12.14% + 3 b) Find f(2). (1) 7552/): «191-3 (v) +5 = ‘9‘—éf§ ; 3 M c) Find the difference quotient and simplify. %(L¢A/»—F(z) 3 Qchk +2) / 3 A A AHA, , {$ch = LN <3) “7:“ ' Z ,9. d) Use the difference quotient to find f’ (2). £9»; (it/+1) : 0 +1 =- / (3) lid 5) Mg; {xz‘w3x+5) = Lx~3 aux: 9,: zcw~3= l/ 5. A snow removal company earns an annual profit (in thousands of dollars) of 13(33) : 0.251:2 — 33: + 100 where ac represents the number of customers in hundreds. a) Find the yearly profit if there are 400 customers. waef (96%): O‘RC‘I)”‘Z~ 3C¢}+/OO W 39/ m b) Find the marginal pro 1t at the 400 customer level. W?J:/f’(a€)t‘filx:3 [WW Wadfi’f: , (4)»3 z/e/B zl‘f’ (6) \\ 9/. 7, <3> w/fi/flm) 5 “/‘9‘00 c) Interpret your answer to (b) Give full units. Mat/7 151--Second H0ur/y—s’13—page 3 8. The demand for theater tickets depends on the price. The following equation shows the number of tickets a: in (hundreds) that can be sold if the price per ticket is p dollars: 3669): x = 100 — 0.005102 a) Find the rate of change in the demand at price level $110. “db/M4 Wotazw 15/<P)=~~.oor(2ir) (6) OJP=HO: ~.905{2L0)2 ~/./ 7(/ b) Explain why this value is negative in terms of the relation of price and demand. \ N WM tin/v WW%/ (3) (105) fi‘OI’f wwwwwqflp gamma/0M [/0WW W 54, Wt fa.) bkL fZZH/W at am M M #0;me W Zzéew Math 151——Second Hour/y—s’JJ—page 5 ...
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