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Unformatted text preview: Math 16A (Winter 2009)
Kouba
Exam 2 KEY Please PRINT your name here : ___________________________________________________________
Your Exam ID Number ____________ 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY
WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS
A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM
ANOTHER STUDENT’S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR
CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE
KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE
EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK
YOU FOR YOUR COOPERATION. 3. No notes, books, or handouts may be used as resources for this exam. YOU MAY
USE A CALCULATOR ON THIS EXAM. 4. Read directions to each problem carefully. Show all work for full credit. In most
cases, a correct answer with no supporting work will receive LITTLE or NO credit. What
you write down and how you write it are the most important means of your getting a good
score on this exam. Neatness and organization are also important. 5. Make sure that you have 7 pages, including the cover page. 6. You will be graded on proper use of limit and derivative notation.
7. Include units on answers where units are appropriate. 8. You have until 8:50 am. sharp to ﬁnish the exam. 1.) (7 pts. each) Differentiate each of the following functions. DO NOT SIMPLIFY
ANSWERS. a.) y 2 3m+x_2 +511 (2614—57 2‘ d.) f(m)=a:3sinw~cosac WW WM]
D 1 .1 . 3 3  
*3? $é<2zéximxmx+ X. mx2wx+ X MX WK
2.) (8 pts.) Solve f’(a:) = 0 for x, Where f(:1:) 2x4 — 8x2 . .9.» 41(6) : (49(3 léx 3) (8 pts.) Solve f’(a:) = 0 for 3:, Where 0 S m S 277, and f(x) = 2sinm —— \/§x. Q» ~P‘Cx/z; RMX~W§ =0 —> 7/?
004x31: ’a 4*;
7
Wu“
ch U17" T
b/ 6 4.) (8 pts.) Sketch a graph of the derivative f’ using the given graph of f. 7 $— ZL' f(33 + A56)  f(x) 5.) (8 pts.) Use f’ (m)— — Aligo A3: to differentiate f(x) = x + 3 .
_ x+Ax _, ><
¥\<><)~ M x+AX+3 “3
AX—> o M (W )Lx+32  TCK+AX+3JX 4’” 0 LK+AX+ 3) LX+3J : M ﬁWﬁeﬂRM 2</%:‘);*% 4°90 CK+AX+3) 0% 3/ AK
‘ M 3' M
‘ Ax—ao CX+A><+ 3’) Q<+ 3] 79K
” 3 __ 3’
— Q<+3j (Ha) ’ Q<+3/ 7‘ 6.) (8 pts.) Find all points (9:, y) 011 the graph of f (m) = x2 — 3:5 with tangent lines to the
graph of f perpendicular to the line a: + y = 2 . SLOPE 01W KW“? a th‘KJN‘ iv
m:( M 340105: of J—M X4 [Mﬂij #Cx :cixv3 a (RX—3:! > RX:<1 A X152] jetml 7 ) (8 pts. ) Determine an equation of the line tangent to the graph of f (x) _ m2 —— 33: + 2
at a: — —1. e—e¥&2: cw< 3 ‘Ar’5L0p5‘%«taﬁj*“§L M20 m:~?612:2(~/2 3:'/~ j~é: ‘5/CX+I) —>
jé:—5’Xv5’——% yz—5X4—l 8.) (8 pts.) Find all points (:13, y) on the graph of f(:£) = 4x — x2 with tangent lines to the
graph of f passing through the point (2, 5) . M, L. Ad
M 92~><
~, 5,quva]
9~~ X
: xl~4x+5'
a~>< 9
IL] m:yl: q~2x J
x’iqm—f: q_ ax—> xiwm—f
avx 9.) The given graph represents the amount of money M (in $) that you spent during the ﬁrst week (7 days) of winter quarter. i y.. i i . , i , . .i .. . _
. , = ' . _ 2 , ‘ '. (5 pts.) Estimate your average spending 1' ﬂaw—e, (0/0)) (3/3767 M
ARC/3 375/0 1 iﬁlasi/W 3.. ate ($/day) for t = 0 to t = 3 days. 3~o your instantaneous spending rate ($ / day) when t = 5 days. b.) (5 pts.) Estimate —,__;_,Wc iii— z$
IKQ ,. 3V3~ qg/Aogé c.) (3 pts. each) i.) Estimate the speciﬁc time t at which you are spending money most rapidly. ii.) Estimate the value of this rate.
L. ] ‘E z a W 3 W .. 61
u») :xzc, : xx 2: ——;§ = Moo/do; ‘ EXTRA CREDIT PROBLEM— The following problem is worth 10 points. This problem
is OPTIONAL. 1.) Determine the area of the semi—circle inscribed in the given isosceles triangle. ...
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 Spring '09
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