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Unformatted text preview: Name: MA 1021  2007 A Term Section A02
September 17, 2007 Quiz — Sections 3.2, 3.3, 3.4, 3.5 1. All students taking MA 1021 in A Term 2007 will take a common ﬁnal
exam on Wednesday evening, October 10, 2007, and should have already
cleared their calendar for this time. 1‘ FALSE (please circle the correct answer — 2 points) 2. For two continuous and differentiable functions f(x) and g(x), the
derivative of their sum [ f(x) + g(x) ] is the sum of their derivatives, the
derivative of their roduct f x x is roduct of their derivatives but the
derivative of their quotient [ f(X)/g(x) ] is NOT the quotient of their
derivatives. Musr use PRoDucr RULE of" D ERNATIVES
TRUE 01' FALSE lease circle the carrect answer — 2 points) 3. The maximum value of a function on a closed interval [a,b] must occur at a
point where the derivative of the function is either 0 or does not exist. TRUE 01‘(please circle the correct answer — 2 points) Com—b occult. AT EITHER ENbPowT 4. The derivative ofthe function f(x) = x7 + 7x6 — 32x  5 exists for en
real numbers x. 01‘ FALSE (please circle the correct answer — 2 points) 5. A function which is continuous on a closed interval [a,b] is differentiable at
every point within that closed interval. TRUE 01‘ (please circle the correct answer m 2 points) Cow—D mk L late“ 73115
{1 P/ease [Pave
ﬁnger am at... as, D
amenable Am J 5° 3 CW 56m 66651 page here J 6. Find the derivative of each of the following functions (5 points each) a. f(x)=x2—7x+12 f/(K) 1‘. 2X”? )53 +336 b. x =————
g() x2+8x+15 9/(X) 1: (3X1+3>(x1+8x1_ [5) __ (x5+3x) (2K4_ W (12+ 87: +6”); 4 C. h(x)=x2/3—W+37r2—7x
x In x)», 3K 17+ X There are four more functions on the following page; please ﬁnd the
derivative for each one of them. Q ﬂ xxx): 21 x—3 92x
(xlﬂ3)z' f/(K) 7 g. f(x)=—2x5 —5x“2 +x3/2 — OWN : 3x—3 A cylinder made of ice begins to melt. Initially, the cylinder has height 10
feet and base radius of 20 feet. The melting happens in such a way that the
ice continues to maintain its cylindrical shape and its heightto—radius ratio
remains constant. When the base radius of the cylinder is 4 feet, the height of the cylinder is decreasing at rate of 2; feet per minute. How fast is the
71' volume of the cylinder changing at that moment? (Spoints) S§flnl¥nét 415 Wj ’ dé 8. A perfectly spherical balloon is being inﬂated. Its radius at time 0 is 3
inches. The maximum size the balloon can reach is 18 inches — it will
explode if any air is added after that point. Within these limits (3 S radius S 18 ), the radius as a function of time can
be expressed as r(t) = 3 + St , with tmeasured in Seconds. a) What is the domain of 1"(1‘)? (4 points)
{:2 O '= f‘ ’5 .3 \ almond/x” oé ‘E‘ E“ 3 b) How fast is the volume of the balloon increasing when F1? (8 points) AV; 4f rh’; 3+5":
31’” air our éJ—TA 5‘
\Je‘ ig—TFFB At”
all] ,LETW?’ 9. For each of the following, ﬁnd the maximum and minimum values attained by the functions on the indicated closed interval. (6 points each)
a) f(;'c)=x2 +4x+7 [~10]
357x) ': 2x+ Ll é— emsl3 at?“ all 7: .23 01mg.“
WW); 0 when xs—L ' — 2. o
le’u'al PDLHl—S: X; ~32 K, 1) x
x «3 1+
7. 3 é—— Minimum Valuﬁ
O 7 6" m“"\m9m Value b) f(x)=x2~6x+5 [4,10]
exists "Rsr all y l:'\ doma‘,n
£150 '2 (RAML: ‘6' I a (“1,1 1 6 no? 13‘ ADMRH‘;
£(X)/O Ian—x 3 Thu; neviac J Crlhcal weﬁcl 2S
Lf~ "3 é._ m1“..me value
'0 LICS/ <’= mos)clvnum Value
'ﬂqere 13 one More parf A; 2‘11}; prawnml D c) f (30:52?” —x” [—1,4]
._.l/ ,5. 2'/3,
1: J2 )K v— 3— X 5+0: 6 «=— Maximum— O 4.:— M\.v\\muw_.— 0""0'1 5 W3)— 973’3 2 mm c: Lr. 8 5(16’31— W c9)(t+%>~(a)[~r"’3)z LP”? 2: 2.5% D ...
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This note was uploaded on 10/13/2009 for the course MA 1021 taught by Professor Tashjian during the Spring '08 term at WPI.
 Spring '08
 TASHJIAN
 Calculus

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