03_notes_20101021thu_mac2311-82489_f10

03_notes_20101021thu_mac2311-82489_f10 - Thu 10.21.10 MAC...

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Unformatted text preview: Thu. 10.21.10 MAC 2311- 82489 @ ChALC:jE - 12f m f [E] WWW . Tesf "" Di *2. "' 3951' fivafi'ire es‘l' 1 fl Del-"ESE _. 1‘? CD jf-ch){scon'b;1uous @ c is a. cri'Hcal pa}n+ (a?) a( f‘ @ - 3C is diflerenfiaHe first! x in Same. Ihkrval containing c (exctp'l') 7555.16ng m‘ c iBelF). @ as 2: "moves ” 52m“. leF-f 4-: rtfih‘l’ “across c” W1 .‘O I G "Then [El .124? f’ckauges from neg. +3 yes. a+ cJ than :9 has a lcc.min.wf. @ C. IF f’chauges from pusd-a ne3.o.+ C) then f («as a ([email protected] (3:! If £.'c{ues m'l- change 95:6 63 C J fish 53 has no Coca! ex'lflemum @ c, *-—-—-——-—/\,~ mm ExampEL @£§4.31'p.239: #5! @ Crih'czf Pb 4,0 ,0? (B an wharf _ I'm-crush :3 f :hc/dec ? CC) ’4')" wharf- PB (If “flakes 30 assume lac. mast/min? Givw 9c ’00 = (x- 02 OH 2) Cont" V ‘Tt. [om/Lo f Sam 1:: 52+ regammgsm. = a = f”: (st—072:”) jl'elds x=~l (mullaphufi, z) decreaswig 'Il'ncfeasfng E] l 5" 455mm” .1 (anal minimwm ualux 4'} x=-'2. P J— M -_—._.____.__ {v- I [:5] 54.5: 3.299.- Hc] Show {hf 3(a): 55E» (:3) I has foe. E”):me values at o 4.. 65 TC '6-=O anal-9:5 and Shh whl'dfi kinda sou-u a] " m) =- €- (-2”). (Z! o=fi?6)=—§-cos(:g);, mg)” J. g: g-l-EITJ {1:3 0,52,... .’. ~62 7Z4. 2;]? #4 £45 no local 'exm‘rema on the open interval Co) 7r) Which/go D3. . Thus fine exl-remc wines occur a’: five 76kb, 43 am! 71‘, fi(o).—.-o amt 61(75)::5 { g(9)__55m(_§:)} ms #1 fins 4. (m! minuzI-oF 0 ad ego and a. local max. wt; of 5d- 6=7¢T , 71168 are aka abs. ezkelna . IV“, ————-———-——--—--—— Iv» _____.._.._._. I/ /" (Q $432 3. 233m 2?! mfmtals (ha/Ace LE fl elf-RIM: values§ when am an? absolm? E] Chic ,’ th3= 1"” (75—4) d- JV 2911! El oi-fi’cx)- 1'“ Zz-F-s'x 3(22—4) 4/3 2_ 2 2— z a = 21 + 3 __6x._ “(m4 = '11:: 1-“ 39C 31 Bx adixi‘o ?XZ-4=o) x2:—$-3x=;l_-_‘% iii CF”: C:“%) C=OJ (.3:ng . ii 5, ‘ J31 neq ,1 "e6. I )i Pas/fl Ni PO E '"i-{z' k : {N Ji/z I F} -t ..g__ 0 3- N3- VG- mar-9851M (aim) decreasinq a9 «55qu @ . Thus f, has . (or ,._.__—— a {06, Minn/2L Z {GPFW ek’ek.l F 5"" 4+ 1:..g... 13 fi' 3 ai- x=_J}= M —?.... ‘+ J fi)“(—.-_7;.)"’ 4 (-—-- > 3} 4 fl '— fiav‘tz’C‘fli—4) “2.”: 3 z w x + 3. ‘23 25¢ 303 N "" 3.123 ...
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03_notes_20101021thu_mac2311-82489_f10 - Thu 10.21.10 MAC...

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