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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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