hw-due-10-19

hw-due-10-19 - SECTION 4.3 1. f’(1:) : 3::2 + 3 > 0;...

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Unformatted text preview: SECTION 4.3 1. f’(1:) : 3::2 + 3 > 0; no critical nos, no loci! extreme values 2. f’(x) : 83:3 — 8.7: : 837C122 — 1); critical nos *1,0,1 f”(x) : 242:2 — 8; f"(v1) ; f”(l) : 16 > 0, f"(()) —8 < 0; f(0) : 6 local max, f(—l) : 4 local min, f(l) :2 4 local min 3. mt) : 1— 3—- 2. critical nos —1. l x . . 2 f”(a:) : f”(—l) - ~2, f”(l) 2 [(—E) * —2 local max, f(l) " 2 local min 6 2x4 + (a I : - - I - - 4. f 1: 2:1: 4- E r: 3 ; no crztzm! nos (note: 0 is not Hi the domain of f), :1: no local extreme values 2(23+1) H ] 1 V-v- . 9. flm) 4—m, critical no—é ! -- . coed-09+ o++++o++o _ _ _ _ _ _ _ _ _ _ _ _ _ __ max _.H...._._o__—o—_o—.p ff: —1 _.l o I 2 max x2~16, :c< —4 2:3: I < _4 10- fix): IG-xz, ‘4Sx<4 f’(:c) : on, *4 <x<4 2:2_16, 3:24 2:5, $>4 critical nos —4,0,4; f(—4) :7 f(-4) w 0 local minima, f(0) * 16 local max 3 4:15 . . 3 7 f __.__- — l 16_ fl(x):(1_ I)ll3 _ %$(1_ x) 2/3 __ 3(1— LEV/3, critical nos 4, 3 f; + + + _ - a - i no local extreme at 1 ; ___________1_,___.|__—-————»—a' 3/4 1 17. f’(.z) : ézUsc-l- 12)($ + 3—2/3; critical nos —2, ;¥, 0 ‘ 1/3 fl. no) : mm min . _ J: 9 , nu anal-emu 7 "M" “I 24. f’(2:) = 1 — 25in 2x; critical nos f(L1r) z 1 1(3— local max 12 12 2 — — — — — — .— + + f’ ++ f(f‘—21r)=i—;r—§localmin 0 1T/12 SIT/12 . . 3 26. f’(x) : 2 sins: cos 3:; cr‘m‘al “05 157“ W’ 57f + + — - + + ‘ ‘ fr. __|___._L....——---L———-—-J—“'—'P' ‘ 0 n/Z “ 3“/2 for) i 0 local min WWW 34. f has a local maximum at. a: -: 0; f has a. lowl minimum at a: = —l and a: t ‘2 35. (a) (b) E SECTION 4-8 [Rough sketches; not. scale drawings] 1- fix) = (-"E -” ‘2)2 fWfl=2W—3 f"(.’l:) : 2 ft ——————— ——ao+++o++++4 2 x ff’. +f§*+++¥00f‘+++++9*+ I 2. ffi)=1—lx—2V "VM-fiwfiummmmmmmmflmm " ' " Hr.) : —2(x — 2) ’ ‘2'" mt) = —2 ‘ f,_ + + + - — - r 2 H f I + + + + + + + + 2.172 ‘ 9 - __ f -2 f(.rl r + 1 NDing+n i f”) {I l 1)2 I . 4 2 “(l __ l l f ‘1”) (r f U3 /'l f: +++ ——- +++ l ; 4 o / l P E i - — - - + + + + g f”. ___.____.1_._...___—-—-— / I ——1 asymptote: y : 2x 7 2 1 q ;_ I; 3 a3. f(.r) H” + 3V 5 . I f’( 5-7 ’3" "4% i "r' " {-r + 3P l l [A 30. f(.r) :00833:+6a)sr, are {03:} f’ -~ —3Sin:r.‘(cos2:r + 2) f”(r} —9 cos"5 .3 0 1! fr! — — - - - + + + + —____..._._.l__....._._._..._ 1’. 2 31. x cm‘ .3, .7: E KL 1:} f’(.r:) : —v1(m3:zsinr f"(x) :: 40052;: sin-2:1; 1 cos2 1:) i - — — - — - - —~09‘1+or4+4+ ' O—-——-—o———-—O f' 6 E x 2 ——0+¢1¢++O¢¢¢ov+O-- U. - H—‘——.—. f O E E K 1 6 Hm I -?-*2I+a:“ 1:<O_:c>9 :L‘ z . 7 . _._, 38. f\) {4+2x_£2’ U<$<2 r _ -2+23i, ICU. 32>? f(vr)h{ 2—13, 0<as<2 { 0 v- . r} futr) ;_ .4, .4. < O, .L > __‘ _2: 0 < I < 2 ++ —-—-+++—— f’:.__.x____L._.__._...L...__. O 1 2 f” -- ++++++ -- :«—»—-_l__.___........_.1_ 0 2 4—33? £xl> 1 39- L: ‘ ms) V22”, ASS} r _ _2-'13, III>1 'HI) { 2x, *1<;1::<1 frr{r) :_ {—2, > J 2: +ooovdne————a.4+,¢n¢_-_-- I f: ———-—-o——_+.._._ . . “I 0 .I x ——-——dm¢4++++o+odne————— —1 1 z Wwwmi hMMi-M - “my #4 -:.-a.- d ...
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This note was uploaded on 04/17/2008 for the course CONWEST 101 taught by Professor Arcilla during the Fall '08 term at NYU.

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hw-due-10-19 - SECTION 4.3 1. f’(1:) : 3::2 + 3 > 0;...

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