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BC_MAC2233_2010_0713

BC_MAC2233_2010_0713 - MAC 2233 Quiz 8 MULTIPLE CHOICE...

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Unformatted text preview: MAC 2233: Quiz 8 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. J a 8" a’EJ-ﬁ31‘li‘ 16121.20 - x — 3]: 7 — :r. .— 4 3 gar-El: J"? at a}; d-i— 3 d:- Evaluate dvfdt for the function at the point. 1) x3 + 3.53 = 9; dx,.-"dt=—?rr x = 1,: 2 l} 4 4 _ f‘ A}: [5) -7 U -i .7 J 4 Solve the problem. 2) Su ppoae that the dollar cost of producing 3-; radius; iﬁetk] = {it'll} + 3th — {12);2. Find the marginal L‘L'Jr'at 2} Cfﬂ=3mw+x crow): Brag-(var when 4U radia'rﬁ are produced. [5; —SI48{'J C} 541’; D; 5142-40 _ I. L}, 3) The area A = '.-'[r2 of a circular oil Spill changer; i-vith the radius. At i-vhat rate doer; the area change 3} with respect to the radius; when r = 3 ft?1 =_ 1LT!" =1 .2 = 6 1T -2.-- .. -2.- f“ 2.-- la. -2.-- Li tt ,.-tt I3; 3.4 tt .-tt air L} 6 ft ,.-tt D; rt tt _.-tt 4) The driver of a car traveling at (it! t'tr'FaeL‘ Suddenly applies the hraker‘s. The Pt'tﬁll'lﬂl] of the ear i5 4} S = frtlt — 3t; t seconds; after the driver applier; the brakea. How many ﬁE’CR'l-lltlﬁ after the driver applieﬁ the brakes; LlL'JE‘F: the Car L‘L'Jnie to a ramp? t WW J : 0 A} ('10 sec IS) 20 SEC C} 30 sec 3; ob: i g 0 ’__ g D "4,15 "= 0 Find the second derivative. ail-£— “ (at '6 0 1 1 1 .2 t: 10 MAC 2233: Quiz 7 (Take—Hume) HURT ANSWER. 1Ff'ir'irite the ward 0r phrase that best cnrnpletes each statement or answers the question. Shaw all wnrk LEARLY in the space provided. nlve the problem. Round your answer, if appropriate. 1} The radius i'it a right eireiihir vii-'iiiicier is iric‘reL-isirigr at the rate t'Jf It]I ins-"see, 1while the height is decreasing at the rate (if '? ins-"see. At i—s-‘hat rate is the i-‘t‘ihime (it the Cylinder Changing i-i-‘l'ien the radius ist'i in. and the height is 5 iii.'? Leave answer in terms (11:21: [that leave TL in ytnir answer}. Ansi-s'er: ind an equatinn (in slnpe—intercept farm] fur the line tangent tn the given curve at the indicated pnint. Give exact timbers {that is as integers or as simplified fractinns in prnper nr imprnper fnrrn}. Find an equation (in slope—intercept form] for the line tangent to the given curve at the indicated point. Give exact numbers [that is as integers or as simplified fractions in proper or improper form}. 2 x3-‘2=4; {4,1} J i r ‘éild't, Increasing and Decreasing FuncTians C F‘ |7Q 92L 3-1) LeT T be a FuncTian defined an an inTervaI I canTaining painTs a and b: 1. T is increasing an I if whenever a < b, Then 'Fﬁa) < ﬁb}. {ThaT is, if we increase The x Then we increase The v. 2. f is decreasing an I if whenever a t b, Then Tfa] > fie). (ThaT is, if we increase The 9: Then we decrease The 3;. 10 is Mere-isn‘t; cm (Loam ﬂaw, an (Esta) 1C is Jenna’ij (9‘15), . Theorem: LeT F be canTinuaus an The inTerval [a, b] and di‘F‘FerenTiable an The inTerval (a, b). 1. If 1" x1) : 0, Then T is increasing aT x1. ( 2. If T'ixlj < G, Then T is decreasing aT x1. 3. If T'ixl) = 0, Then T has a harizanTal Tangen'r line aT x1 [ThaT is, f is Turning aT x1). 162.20 :70 when jig-(a gr“ 353,13, 1930 <10 when amid}: f F230: D J 13\$ «and 1319 SD Ice):0, 7cib>ra Extreme Values of Functions Absolute Extreme "v'alues iExtrema} (a) Absolute maximum: Highest value of the ‘Funotion on a domain. (la) Absolute minimum: Lowest value of the function on a domain. Extreme 'v'alue Theorem: L t R “5 . . . . . n :9 u Mir-time Condition: 1‘ Is continuous on a closed Interval [a, b] "m Then: '1‘ has a maximimum value and a minimum value on the closed interval. Looal EXTFEmE Values: {a} Local maximum: Highest value in the "region". |values Just to the left and Just to the right are lower. (b1 Looal minimum: Lowest value in the "region". Values Just to the left and Just to the right are higher. Critical Point A point vvhere there could be an extreme value (absolute or local): - At endpoints {where the function starts and ends) - At turning points (the derivative is zero: t'(x] = 0) - At singularity points (where the graph has sharp points: the fLIHC‘l'lﬂflle'iﬂS a value but no derivative at that Din-r]. +Lafﬁl-ﬁ DID-lug: rIi..L—-—-_";>‘-a--. .4 HFIT} FEM-a P 3'. | . J M, ﬂqffﬂiruﬁ Er‘ln’i'rm'ml J—I—LL} Ex. 3.1 (p. 179). Use derivatives to find where the function is increasing and decreasing. Nate: 1. Intervals aver which the function is increasingt'decreasing are x-intervals. 2. Intervals far increasing/decreasing are always OPEN intervals. [ 1601.): alt; 3:3 - 3 3‘- Step 1: Identify et't'tteel values: These are x-values at which the function can have a relative maximum or minimum: QO’PDE’JB : “one - Endpgints fusuallv given or easily identified) ’ I - Turning paints (where the derivative is zero). 71“ qinj Pant: 10¢) _-_ D - Find f'(x) and set f'(x) = 0. Then solve for x. The x is the critical value. I éx) : :3“ x2,_ 3 - Singularity points (where the derivative does not exist). (1,. 50+ £33) : D g It- 3 = 0 Step '2: Set up e tebte es fellows: 4} Raw 1. x values around the critical values ésc’l’” {‘1 Qlixlrii Row2=f'(><) ‘ j— 9‘ 1 3 Raw 3: A sketch representing the sign of f'(x) Ianllﬂ‘ x : L}— We as; )C '-'- i Q 5” M5 is w H) we: some mm A... (“Had 5, Step 3: Use the sketch to L/ ““"W x] identify regress of increase a decrease. Ex. 3.1 (p. 179). Use der‘im’rives Tc- find where The func’ric-n is increasing and decreasing. %‘ _,_ l1 :1. f )YFLQ“SE1TV ‘56? {09:0 . 2 z ‘J" wipvtd‘s / ,1 +231. :03 B113 0 hf Turninjfniahl ¥ZK)=UIU"UV (11,01. "ngw:0 1 r “I 5:: 111.2120 “(REFX “(\$3323. 0 W ITZMO Fae! MJLM if (x) D“? “L 2x ._ 1(2):): 2x1+2171 Lead/L? VJ ii?! 1 1' 5 “:3 1‘5“! i: i 3 wow 339*“ O 7 Z )1 7—1 OK) “’11—— ;d‘xJ- I x7721", 0 GM 1 ﬂamahj on: ('90: ‘2) “and (019°) :DLM'E-asinﬁ ﬁn? ('2; FT) MA (43 0) Ex. #2 (p. 189). Find all nele’rive ex’rreme for The given fune’rien. If The fune’rien is defined on a closed infer-ml, find all ubeelu’re extreme else. 39 loo-=2 (1’3)3 la”) 1(01): £4213 ND Enwalfeihﬁl "a alﬁdmll‘l Mo: Mae-2f '13- NT} arr C’ Li“; : --| e—Ahsaiml-Q “at. VU - “(ﬂat uztm V(Ctj:l h'¢*)=(é~2) 1: n :‘ a; M . % f (t-RJ'Q _2)2 HESD/“je 3 “’C)=0: -z __ MW W5): 5/ («t-2r” 3 ﬁfaf’ﬁl'blt r" {340 W “(hag Ad 75-“? £5393] ...
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