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Unformatted text preview: Math 16A (Winter 2009)
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Exam 3 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 CODETO, 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. N eatness and organization are also important. 5. Make sure that you have 6 pages, including the cover page.
6. You will be graded on proper use of derivative notation.
7. Include units on answers where units are appropriate. 8. You have until 8:50 am. sharp to ﬁnish the exam. 1.) (6 pts. each) Differentiate each of the following functions. DO NOT SIMPLIFY
ANSWERS. a.) y = (3x + 1)—7 v D 1 U8
‘ ——a Y :~'7C3><H/ L3/ I wf. wee/cw (Kw/(w (76 q) 3‘
c.) y =tan2(sin(4ar)) J M/ M/ qX) 2., ’x/l: QMQM L4X22M'zé4i’ﬂ God/ MGM). <4 2.) (5 pts. each) A ball is thrown straight up at 48 ft. /sec. from the top of a build ing which is 160 ft. high. It’s height h above the ground after t seconds is given by
h(t) = —16t2 + 48t + 160 . l . a.) How high does the ball go? + : ——’ : 3
WM; maze A f .39“ hlﬂ'):'32wé+"3=° , M
he): Wei—2+ «ye/wen: we
wlongistheballinthatf:o A “lei—MP (Nae +IGO : O __>
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f : S'M. c.) What is the ball’s velocity as it strikes the ground '? LUCK}: ~35z®7+qft *1/12 435/“ :3.) (12 pts.) The area of a Circle is increasing at the rate of 16 in.2/sec. How fast is the
circumference of the circle changing when the radius is r = 4 inches? AzTY’V‘J‘ 1%:(5Mé/w ‘ M )
C:2'W/r/ . ’vt FM: EEWV‘:<{M4 .. 2 D (Am A 1TV‘ —_. ._, ~ i
A I» (M  SLTFV‘ Ma lécin’é‘l/
air 3?. _ D
—>,(;_;_1_\,M1:;’/ W CQTW—a 4.) Assume that y is a function of :r and 6x + y2 = my + 4 .
a.) (5 pts.) Determine the slope of the graph at the point (0,2). 2—»; C+2Y7’: XYI+CI2Y —> RYYLXY(:Y~G _._>, C51Y~X2YII Y~Q MK:0}Y:2' ‘ i0 1: 3‘6 ‘ :fi : “ ‘
4‘0" 5L0 5 Y Aggvo H l b.) (5 pts.) Determine the concavity of the graph at the point (0,2). a Yu: Wt meme
Cay‘xjk Y:~(. ~/ 40—“ II Ya we)» ewes) _ ~12.
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c.) (3 pts.) Draw a rough sketch of the graph near the point (0,2). C0; 3/ 5.) (20 pts.) For the following function f determine all absolute and relative maximum and
minimum values, inﬂection points, and x— and yintercepts. State clearly the x—values for
which f is increasing (T), decreasing (l), concave up (U), and concave down Neatly
sketch the graph of f. f(:r) = (1:4 — 4m3 ON THE CLOSED INTERVAL [—1,5] .2—5 +220: Ami—(2961: 4Xl(x~. 3]: o A 4
X:~/ X:0 X13 K
 '5’
Y: 5/ \f‘0 Y: ~01.7 Y: lab“
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D ll 9‘ flu4 ’l‘ngm 3<X<53 41M \L,&w {<X<o/o<x<3/
\Y—wu/‘yy ~l<X<OJA<X<53
Aha /] 4,7 o<><<2c) 6.) (11 pts.) Determine the x—values for which the following function is increasing (T) and
decreasing DO NOT GRAPH THE FUNCTION. f(x)=w4\/E
1 D I _i 4x 3; l 27.32.
\ ———>~QCX/:l~4 ax _ l» 6?. ()3 if);
3 X'KZOQW*&:O "566‘12—5
M2 // 80
><=<I ////1'[ M O ‘l’ 4: 7.) (11 pts.) The radius 7‘ of a right circular cone is increasing at 4 _cm./sec. and the
height h is decreasing at 5 cm. /sec. At what rate is the volume of the cone changing when 7' = 3 cm. and h = 2 cm. ? Assume that the volume of a right circular cone is
V = (1/3)7rr2h. obk' / EQLCMM b13w/l/lzézm
00F EXTRA CREDIT PROBLEM— The following problem is worth 10 points. This problem
is OPTIONAL. 1.) A large grapefruit is projected upward from the ground at 160 ft. / see; How high does
the grapefruit go ? Use equations given in class to solve the problem. Mgr] ; 4679M (we
———‘r ——» M5] : M/é git/60657 : 400 ...
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 Spring '09
 GILL
 pts, Convex function, right circular cone, Exam ID Number, University Honor

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