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21Test2A

# 21Test2A - boLUTIOWD MATH 122 SECTION 021 TEST 2A Show all...

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Unformatted text preview: boLUTIOWD MATH 122, SECTION 021 TEST 2A Show all work for full credit. Good luck! 1. Let H (t) be the height of snow on the ground (in inches) as a function of time in hours after midnight. How would a weatherman describe the following statements? Be sure to use units in your description. (4 points each) a. H (3) = 4 4+ 39’“ W x: H Inches 00 5mm on M grand. b. H’(3) = 0.5 [565mm 3AM am} 414/” we @9054 an Mfg/[howl 0,5 MCI/Ids 0? 5mm ac’wMulal—nm. c. H’(14)< 0 I‘ll 29/1/11 He helyhl 00 6mm) 0/? lie grand Will lac deCi‘CaSl/Ij [[6 he Swan 15 Wilma), 2. Find an equation of the tangent line to the graph of f(w) = 9:2 — 4x — 45 when a: = 5. (8 points) pawl! (5,40) 94/014740 \f’ (#0) =&()( ‘5) 1%): 25-20-45 m) = Zx-‘f wL/o = (ax ,50 2 '40 P’[5)=/0—4 l ;= [0X'70l =10 3. A model for the temperature T, in °F, of a typical spring day is given by T(t) = 40.72152 + 8.22: + 49, where t is the number of hours after 8AM.iS the temperature g 011335111? . o 7 - r at a. of 4.6 F/hour. (8 pomts) [£3 7 P0591“? 241C henmlwc , _ MHé +8.2 =49 - - =3 T/t) [.L/L/lé th __/.44£: 13160 i = 25 Am ally 8M1 2 4. Given the graph of the function f (as), sketch the graph of the ﬁrst derivative (Wm) 1mm £00 Mo [—wféo) MC, — X: -[p MHA O + (_(p"5) l/lC x: :5 M“ o (’3) 2) WC, 0 X=Z Mm + Inc 2 (a (xidp> ”W 0 (£0,003 Bee "' 5. The graph below shows cost C(q) and revenue R(q) for some good. Should the company produce the 40th item? Explain your answer using marginal cost and marginal revenue. (5 points) l10000 35000 30000 25000 20000 15000 10000 5000 051015202530354045505560q 3 CW Rm) m marﬂlﬂal 505* 15 gr‘c’alt’r W” “4-6 Marginal revenue at 2:40. (We CM Jae” lad Compannj m 5/0/25 of We l'anjenl Mes) Tie 402% 1km Casls mat MM #5 marlin , So we and wok gmduce +146 llem. 6. Find the global maximum and global minimum of f (9:) over the given interval. (8 points) f(x) = 3:4 — 83:3 + 10:52 + 15 over[—2, 6] : L/Wx —5)(x—I) CnhCal Pct/Ila 3 0, 5, l comm: 10(0): 15 PO)=I8 9(5): to 101m: mm Mo): —5¥ 3 7. The following is a graph of the ﬁrst derivative, f’(ac) Answer each of the questions below. Be speciﬁc — Don’t use ”it” - Say What you mean. 2|] 15 10 -10 -15 ~20 a. Is f’ (8) positive, negative, or zero? How can you tell? (3 points) 10783163“ «0’00 '5 We i“ W's ”he“ ”8' l b. Is f (:c) increasing or decreasing when a: = 2? How can you tell? (3 points) 706‘) '5 ”when X=Z since pYLl 1s (ash-we. c. Is f (3c) concave up or concave down when m = 4? How can you tell? (3 points) (‘60 18— mm. x=L/. WK) Is deems/.3 when X=Ll 50 (”(4) Is 1463mm d. Which value 1S greater f(6 )or f(8 8)? How can you tell? (3 points) m 10 ’60 Is nejahvt OW [(0. 87 whld’l means 1060 is Olecmasmj over [08] e. Estimate any point(s ) where f(ac )has a local minimum (3 points) -U?’+ E M m 4 8. Find the derivative f’ ( ). (8 points) f(x )= \6/_+: - # 7x+\/_ / , ’ X ath ) ¥X+Z (—7 -7 . 950: ix “Ex 2'? +0 9. Find the derivative f’ (x) (6 points) f<x>=-———-= 15(X ”IX ”53 (\$4 + 4962 +1 rm: «as/x”+4x‘+\\$ (mm 10. Find the derivative f’(;c (.) (8 points) :c)=5”” w+1n(8:1:3—10x) My 5 XW/x — I) + /Xx’l:’3/0X> (24x (206 11. Find the derivative f’(x ). (8 points) €6m4+2x —(a:7—x3+2)8 12. Find the derivative f’(x (8 points) (£01m (x771— 83:4) m: 5/W’1 M [x1 ¥ w + 31W) —32ij ...
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21Test2A - boLUTIOWD MATH 122 SECTION 021 TEST 2A Show all...

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