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Unformatted text preview: Math 161 Midterm 2 Name: \5  . Date: March 2, 2007
Instructor: Dr. Paul Choboter
Time limit: 50 minutes Read all questions carefully, and show all your work neatly. Calculators, books and notes are not permitted. Good luck! Question Score Points possible V 1. Find the derivative of f{m) : 3:32 e 51“ + 7’ using the deﬁnition of the derivative.
(In this question only the differentiation formulas earn you no points. In all the other
questions on this midterm you may and should use differentiation formulas.) £00 3x2 “EM—1
5? (K3: M“ 3 mm:  5 LX+h3 :1 “"sz bot—U h—vo .Wm—m
”gunIF' '—‘ Q 0‘3 £190 X+bxh*éhl%"5hﬂ*%ﬂﬁ V _ 1 V 2. Find the derivative of each function.
(3 pts) (a ) f(:c)= —3:r:4 +%+1
.7 my}
$00—— .gx4+2:x r”
”s W): —m3~x 7» /
r : .— 9— 3 — ___\__
H (x) \ wk ,7 "fr—X3 J
(3 pts) Lb) f(:c) ;. $13283 ,5 1  ‘ ,
iJF’QO= ﬁe“ 5% l’f/ $111 .I‘ 5f" 2?? o\ x?) 7
C 3 ;———t::) a); MW
‘3 ii Cx)‘ ~ L (”2) ELK" 5X :jgllcosw j (3pts)(c)f(m)=(1+$3)1/3 # (3 PtS) (C ) HI )= 7“” ‘\ (¥)_ fl COSXX
Coo mm W $2 (03“)
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V (5 pts) 3. (a) any“ +332 y: a: + By Findd — in terms of H: and y. ﬁ CX%4+X1®: QC+3d\j)&( x3w +LE§LX+X€1XUJ ggxx :\+3%&
x4l5a%*\5+‘*ai aﬁ‘Wﬁ 5/ x‘bﬁg %% + X2%%—*3%&14—LA1X dJ
(5 pts) (b) Assume that :r and y are differentiable functions of it. Find —T— when 3:2 +1312 3 25 dt d '2 7: [’1
23C: Mﬂafﬁ
2K% +2kjgi$zo d
M M3? —. "”7:—
5 _,_
d
0C a
a? "' :%”(“13
V— : (—0——
3%
($1 ——57: V (4 pts) 4. (21) Find an equation of the tangent line to y : I + \/:1_: at :1: 2 4. \j I» (a
\5 2‘. 7Q 4r \IX
\5‘; 4+r: 4¥11bﬂmmy€hml q \jmﬂx L \Lﬁﬂo 2%;(x 4 Us \ﬂ‘:\+.\ix 1 ........ _.._._.—— ______ __
— n.
\jf—l 1W ' \ __ .L. h
m 1 ("a '; \ + 2W —' ‘4 k 4
7 3;) 49! 04 O
(3 pts} (b) Find the 10th derivative of ﬂat ) * eT —/2€6/+§z2+)0 ,.»—" i We) : eff i (3 pts) ((3) A particle has position (or displacement) given by 5(t) = t2 7 61: + 11, Where t is in
seconds. At what instant does the particle have a velocity of zero? SCOL’Clubt +\\
s’GO=v— Ztlo
3 O: 2t*lo
Q2 3 2t
JC 1 3 '1' r H»;
5. Let y x 51:4 — 4:33 2 m3(x — 4). The ﬁrst and second derivatives are
3," 2 42:3 w12332 = 4332(2: — 3), and y”212:c2 — 24a: : 12$(sc r 2). {2 pts) (a) What are the :r—coordinates of all the critical points of the function? \5': a”?— (x45) 0 = ‘lxz o
N... X (3 pts) (b) For What values of 3: is the curve increasing? For what values of :13 is the curve decreasing?
'2— a
03 l : 4V (IS—‘73) b) (—0 z 4002" L4“ :3)
V ' 4 (A) 1 "" Us
A of} ___.._ » — ~ ~ +++ [5'03 ”' 4L01(\'®= 9?: X q '00) ~— 4100)" (lo'3} Wan "100 ' #l " (2 pts) (c) At each local maximum or minimum point, state whether it is a local maximum or Ininiinun1_,_____ and State its; (33d 13319314) ( was" a locdl 'm\mh\(iih
gL’D 7. 11(4) = 17 qum “YEW 3 WWW... __ __ _ O, ,.
v3 \3 mcr‘eOtthWJFzSFWC%#§D
decrEQSmci tor (00. ’5 ‘V CL (3 pts) ((1) For what values of m is the curve concave up and for What values of a: is it concave down? Lj H ____ \ZX (Xvi) Lj "(\) _ \2L\)(\Z) ; ”ll o 2 max ~73 (,3 "(—0 : lat—Devwao 3 o 1 0.x 0 : x "7— g ”(m : ammo2): +
K; x=2 w ,, maeup
Arm—Jr ~ ~ —~ HM W on was?) 0 and comm
down on UN 2 .—«~——h_.__, ...
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