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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’EJﬁ31‘li‘ 16121.20
 x — 3]: 7 — :r. .— 4 3 garEl: J"? at a}; di— 3 d: Evaluate dvfdt for the function at the point. 1) x3 + 3.53 = 9; dx,."dt=—?rr x = 1,: 2 l}
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.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; 514240 _ I. L},
3) The area A = '.'[r2 of a circular oil Spill changer; ivith the radius. At ivhat 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'llltlﬁ 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‘reLisirigr 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 ii‘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}. Ansis'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 31) 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 Mereisn‘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 Mirtime
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
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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 xintervals.
2. Intervals far increasing/decreasing are always OPEN intervals. [ 1601.): alt; 3:3  3 3‘ Step 1: Identify et't'tteel values: These are xvalues 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).
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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‘
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L/ ““"W x] identify regress of increase a decrease. Ex. 3.1 (p. 179). Use der‘im’rives Tc find where The func’ricn is increasing and decreasing. %‘ _,_ l1 :1. f
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closed inferml, find all ubeelu’re extreme else. 39 loo=2 (1’3)3 la”) 1(01): £4213
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 Fall '10
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 Nate, J M

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