math221 f02 midterm2 versionB - alérS all-n I MATH 221 —...

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Unformatted text preview: alérS . \ all-n .. I ' MATH 221 — Fall 2002 Name _ ' Midterm #2 -— Version B February 28, 2002 Do your work in the space provided. Remember: no work = no partial credit. If you run out of room on the fiont, use the back of the page. { «(K3 = to x t \‘J. 1) For the follong function, find all relative extre the M011 which the “F “(4) = o = 0 function is increasing and decreasgg, 53 the absolute maximn on the interval [-2,0] .1; a (o) S 0 >0 mm f(x)‘='5c3+6x2315x—-10 591,1} = 330, gum: ‘9 50W“ (‘00: ax’fllx --\6 , a W o= 72x1+nrlg ‘90)): ym \&h o = “3061+th "‘53 {,‘(0 «no ’ 0-; ’50: + 5Yx - 0 x s —r5,t antral #5 flnflwrf (moral—505.0 \ (use) fhcwasmo} ; (-m,-5)Uo,ca) demaiw 9:0 4— 0 "' O + I \ Yetat‘t‘hre “xx—5,401 / \ HMT‘W- WM 2) For the following function, findjlpointsof—infleetion, and the intervals on 'which the function is com; ve upward and concave downward. , obi 1- 1: .1041 - rfi‘ubl- - I .q - “MM—H ----- -“m*---mW'---~---mm "7AM ._ 4 3__5_ 2_ - - g(x)—4x +21: 2:: 5x+23 \‘ con(a‘re “‘0 . '00) L g V ‘00: x1, J‘” bxl— 55‘ -I -1-\ 4%: 0°) I “(:09 Ex; + \‘LX " 5 wit ,W..-.\...‘.H.K.fl_~— -.._~_,__.W;:___-WW 7 O ‘ ’bx" H14"; \ CGMCWV'e dww *2- 3g)"21 3’ Ks, 4'2. '13 vaaX-s‘) , W! WWWMM w (“PH c untied—tum: =' -\1 " 10H ' . s t, rl—G—gi-W’LH 161+? 31% :-\1'f.1\§¢3\ E“ q __ I \o —- _ + 3—" ' 2' " 33- ~th% .23 [-wt) 2 ‘H‘F—S} 41.0\*\M%.DV"L+j-qb+llfl <———P-—-—-—‘—J> .om —~ ,\0’l’l ‘t'aolrltflfi IQ- 3) Graph the following furrction. Give and label the coordinates of all relative extrema, all points of inflection, and all intercepts. ' ll I510 3 f(x)=x5—5x W'S‘O ‘P 10x: 0 tug-Sat «is x90 0-: ¥(x'+ -5) X513? 2315 “0-99 (3 (0,095 w l-___ Vfl‘ (01w) ' (0,05 4) Graph the following function. Give and label the coordinates“ of all relative extrema, all Eoints of inflection, all intercepts, and give the equations of all asymptotes and lines. KM," ‘ — 3x2 “9 . WYA l ! 300* x2 _9 My,“ Fin-lest x = 3 V xv") : o = h . , 033619,» . XL?) r o I X G a) ' ‘ x v 1 WWW J! \ >W‘fiov. (a, o -— -.( w , it I ' aw: be (Xmon— (3x14 no ( xiv-fl 3" 'aé-ia’x -w5+ifi 5) The demand fimction of a certain product is p = 36 — 4x . The cost function for the same product is C = 2x2 + 6. Find the maximum profit and the number of units needed for the maximum profit. Also, find the minimum average cost. ‘P‘ px " C '5; "in 7' >‘___““’. 9* (3‘0 "W3" " (1*1+b7 = —\ox 4rng 40“" ’ 3‘05!“sz *L‘Ka’AO "C‘ -. ..\o How‘- ”7)Kox 49‘9"” 9‘ a» '\L¥ 0 f -\"Lx1'79'0 3b: \‘ZY fl”, 1W 7) Find the derivatives of the following: 1 a) y = 43cc? \j‘ = “eh” 5' 416"" ‘9 (3x+l)(2x—3) (V¥1 J. at '70 0) g(x) = e b) f(x)=(1 1e")! 2% 00 w 8) I recently conducted an experiment in my refrigerator. I found a colony of bacteria that began with 10000 bacteria. Three hours later, there were 20000 bacteria. If I let these bacteria continue to multiply, when would there be 45000 bacteria? : C, 3“” \j; \opooeo'n‘t "5k- ‘Lop a 1: \claogoe “@000: “3,000 60.15“: km “\L'(\V\L \V\ W“- 'D'lja‘b up. 0.13“: ' 0.13M be; lo .5\ Y5. ’_____________,_ 9) The half-life of a certain radioactive element is 223 days. I just happen to have 12 pounds of this element in my back yard. a) What is the decay constant of this element? b) How much is left afler 400 days? \lfl’i'. -: 7,1,?) _ e we ‘3 Cf .. o.oo’b\‘3-Ul°1D —.~ we ' 7 733*“ 9mm” (‘6 ...
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