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Pretest2Solutions

# Pretest2Solutions - Sou/ﬂows MATH 122 PRETEST 2 1 The...

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Unformatted text preview: Sou/ﬂows MATH 122 PRETEST 2 1. The cost (in dollars) of producing :1: units of a product is given by C’ = 3.6%? + 500. Find the marginal cost when a: = 9. Interpret your answer. ' 4’ MK? Cf: L3? ; m we My: ﬂroc/icio/ ‘9' Writs, 7%; angina-2A (YWMWM __ (as; a mom» 7% an m; /5 €35,500. 2. The revenue (in dollars) from renting 5: apartments can be modeled by R = 2;:(900 + 325': — 532). Find the marginal revenue when :1: = 14. Interpret your answer. .4) E: 67an %(}LIXZ,ZX3 2/ we My? ”#11112, )4 aﬂa/Jﬁfgmlb) 7946’ angina/zeal Wade #W Hag 16HA ME: x2‘ = 1800 Hsz '(oxz, . ﬁﬂw}wﬁ} I‘m-ital Is \$24M. Em; .«~*-ng0 + [2309) 12-04): —_ 3. Find the points where the function ﬂan) = 3m3 + 725:2 —- 8:1: + 15 has a horizontal tangent line. Explain your reasoning. 519/ ! f’MA/ Jangm/ [:45 =7 dope =0 :7 1(1 bf) ‘0 For): QXSZHé’x #87 Wyn/Y -3 :0 (7x-LUKX +Z):O 1 2 4. The following data represent the price and quantity demanded in 2004 for IBM personal computers. The price per computer is given in hundreds of dollars. 3.. Find the average rate of change in quantity demanded between 10 = 10 and ‘0. Estimate the instantaneous rate of change when p = 15. Interpret your answer. bud-pm) ; 17/470 ; .25 Z D716) xZELg?" :ECMWWS/hmw AD“: <43 2 . [7—5 .7. '35 +0 {two 7%: airway cleavage; [0% 3 96’s,: 2. 5. The population of a developing rural area has been growing according to the following model P = 2219 + 52: + 10000 where t is time in years since 1990. a. Evaluate P ( 15). Interpret your answer. Fﬂ5)=zz{/s)z;5zlzs)*lm 1” Wilts mama 15 P05} /5 ?30 / 5 730 PFC/015’. b. Evaluate P’ (15). Interpret your answer. P’: W ’:5; gﬁwc’m 2005 and @062, Has populahm 20’“) : Wﬂ5) #52. gram 12.1 WZ maple.— I -W 2 6'. Suppose a‘ function is gifen by a. table of values as follows:I -.---- a. Estimste f’(1.7). 1. my ms) 21-2.; )0 ' " 1.7 L5 .- "0-2 ' NIL 01:; E; 1..- I M?) {‘0 73....2‘1-23' 5. 1‘} H512“ b. Write an equation of the tangent line to f at :1:— -- 1. 7 y 23 2501-17) \{IZS 7,5;{s/Z7‘SI 7. , Fi11-' 1n the blank with positive, negative, increasing, decreasing, concave 11p, concave d0W11 or unknown- - . . . - IfI f’(3:)— IS increasing then f(a:) is M. _ I If f (1:) is increasing {alien fI’(a:) is M“ . I h If f”(a:) is negative then f’(\$) Iis 1' If f’(:c) is decreasing_thei'1f”(m) is_II négaﬁ‘vﬁ . ' 4 8. Given the following graph of f (3:), ﬁnd the graph of f’(3:). i 1 _|n’r€rvel_l WK) \$1000 III-IIIIIIIIIIIIIIII III-IIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIII III-IIIIIIIIIIIIIIII III-IIIIIIIIEEIIIIII III-IIIIIIIHIIFIIIII Ins-Illlllﬂllllﬂllll IIIIIIEEIIJEIIINIIII IIHIIHIIHIHIHIIIIIII IINIIIIHBQIIHIIIBIII IIIﬂﬂIDIIIIIIﬂIIIIII IIIISIIIIIIIIHIIIHII II-HIIIIIIIIIIIIIIII IIMIIIIIIIIIIIHIIIII IIHIIIIIIIIIIIEIIIII III-IIIIIIIIIIIIIIII III-IIIIIIIIIIIIIIII III-IIIIIIIIIIIIIIII III-IIIIIIIIIIIIIIII III-IIIIIIIIIIIIIIII O 9. Given the following graph of f’(a:), ﬁnd the intervals over which f (3:) is increasing, decreasing, concave up, and concave down. IIIIIIIIIIIIIII-III C a m , _ d9) III-IIIIIIIIIIIIIII P5X) ’5 M ”C 5 (f) K 70 '3 U (5’ III-IIIIIIIIII-III #5, F’ Maw III—IIIIIIIIIIIIIII : :::=:::=::::::::==: > lllll-lllllllllllnai PM Is decimal/nos (m,-?3U( ‘)5 Illa-allllllllmlll , Illnallxlllllllzalll a p ’36 aim IIIV-IIIN'IIIIIIIIII 3 =:a=::::i::::&=::: ( 4W 3 ll'l-lllllns-Hl—lll fee 15 caamut “P a“) 1’ ll’ﬂ-IIIIIIIIII—lll , III-IIIIIIIIIIIIIII 4 ,9: Psalms Ill-IIIIIIIIIIIIIII ‘ III-IIIIIIIIIIIIIII a F MCK‘UﬂSMj IIIIIIIIIIIIIIIIIIII Pix} :5 @ﬂmbﬁ 515W ('H,Z) ﬁ ijah vi "’7 p! 5&0?de 5 10. At a production level of 2000 for a product, marginal revenue is \$4 per unit and marginal cost is \$3.25 per unit. Do you expect maximum proﬁt to occur at a production level above or below 2000? Explain your answer. 4,! a .. lama’uohm law) all 2m marginal (“mews excess/s WWW? 605’! Cfmhﬂﬂ 4 Maﬂjmal) ﬂﬁél of \$975 5:»th {all} {0 ’5 iﬂWASaw J 2 W5 EX‘ch-rt Max/Mum ﬂag} *1) 06cm" 5?; a maize/1m level 2600. 11. Find the equation of the tangent line to the graph of f (:23) = 22:1? at the point at which-:3 = 1. ,oo,,,;..(,,-»/z)' ape-ma wﬂﬂﬁZ/(xa) WI): 1;; g, M) (max) mom 7 I 7W1): [2)(22-(4); g, if H 12. With a yearly inﬂation rate of 3%, prices are described by P = Po(1.03)t, where P0 is the price in dollars when t = 0 and t is time in years. If P0 = 1.2, how fast are prices rising when t = 15? P= 1.20.03;c P; }.2 (1.05315 M0033 PYIS) = /. 20.0355 M103) ; WIS): 0. 05520: dollars MW 6 13. The price in dollars of a house during a period of mild inﬂation is de- scribed by the formula P (t) = 8000060'05t, where t is the number of years after 1990. - a. What is the value of the house in the year 2000? m0) : 300mg (9.0500) : ha) 89?. 70 b. At what rate will the value of the house be increasing in the year 2000? M): sweaﬂ{o.05) . M20000 : wowed“); 3‘6")” 25:- Jgi- - /4Z , Mame 0.05 ' 3'8“ CW5 M: 0.05% I d. When will the house be increasing in value at a rate of \$10,000 per year? MDQJ .: We 0.05£(a05) 2mm; .—. 33:: 80.05%; , ) 2'5 .. 225:6 we . LL" 3165 - lime“ A926: Me ' )ﬂ 2003; m Mme am /425 = 0.05% be Imam at a; me. 14. Find the derivative f’(:c). f(:z:) -I—-in(:z:)+5x——4 s/r’iX f5X,X mkg ; 59.45 31's} 15. Find the derivative f’(x). f(£L') : 74x9+5z-1 for): quzis""/ﬂ;z/zx+s)i 16. Find the derivative f’(.:1:). 17. Find the derivative f’(a:). f(m) = (\$9 — 3x4 + 4)7(in(a:) + 3mj3 8 18. Find the derivative f’ F'x 19. Find the derivative f’(:1:). ﬂit) = (\3/5 * 436 + 232)15 .,_...__.,.__.__.....~.-—-— ,_.._n..,__......... .._. _, #u-l‘mum-HWWFW‘I‘W fI/X)JA/f-X4) [)(Z—f){3)'(3x+l)62xj>+ 3w)“ “7X46 6&4)" M!) a 25:2. 3x3” [3x3+x)(2x) #5753 9x2”) (3%” 71 W ; q 22. Determine the critical points and identify each as a local minimum, local maximum or neither. . f(x) = £33 — 12—3222 # 30m+ 15 £160: X2*/3x .30 #153) @ '2 (9 15 C9 . X245}, :30 :0 / x 2 4m Mism- ,2 :o ——-——- l ) ﬂ-Z) lb or loml maximum. X=X5 X=~Z 10/5,) 15 a 106A] Mnmmmt 23. Determine the intervals over which ﬁx) is increasing, decreasing, concave up, and concave down. f(m)=:z:3-—6m2+92:+3 fﬂﬁjxﬂ/ZXM flx’ﬁéaxrll 3 2, _,_ @4210 X Mm”? 0 (0X5): 3(XZ’L’X +3>zo X: Z 3(x 3m ,) :o 5544344 1%) Z X—3 X-I N L) Pix) '” ”4' H I £6015 mama/x [—ml)U(3,w3 ———I-'—l—? 2 5619569 pm 5 /? x, - /7 ﬁx) Condom? up (2,, 093 10 24. Determine the global maximum and global minimum of f (9:) over the given interval. f(:r;) = 23:3 — 35::2 — 122: +1 over [—2, 3] PYX):(pr—(px viz [’mpm: PM) = —3 : 5(XZ'X’Z) PM): 3 global MM _ :Zo(x-Z)Cx+l) 10(2) : 4‘] WM 10(3): -3 Gum Pom : 2,-1 25. Determine the global maximum and global minimum of f(:1:) over the given interval. f (m) = 3:3 — 9m2 + 153: + 1 over [0, 8] {UKULEX 248x H5 impart t 10(0): l 3332-pr *5) pa): 3 ‘7 3(X'5)(x 4) Cal-1:41 Fwy/5: 5}! 26. Suppose that f(m) is a function with f (7) = 25.3 and f’(7) = 2.4. 3.. Estimate f (8). Pot/1+ (3?, 25.5) \vaﬁB =ZH (x571) P{83225.3+2H 5’2 5% Wm q—zs.3:2.4x—Iéo.8 =ng] v; -: 2%: + 815 9(3) 3: z.u.(3)+ 3.5 =12??? b. If the actual value is f (8) = 28.5, what does your answer in (a) tell you about the concavity of f (3:) close to :1: = 7? 7h? 01ch mm is grail-tr ‘Hmm cw eahmai-r) 59 We graph )5 Claire h; X=2 é”Aci7Jr-~.\. \/5‘ ESﬁml-c ...
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