Extrema&Graphing - 5:2 5 3 EXTREM IZN_D CRHPHING...

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Unformatted text preview: 5. :2, 5, 3 EXTREM IZN_D CRHPHING RECBLL : RELfinDE flfiXlflUfl : FUNCTION CUHNGES F900 HQCREHS’NG T0 DECREHS'NG RELBWE mmmvn : FuchloN chances neon DECREDSWG To INCREDSWG ms rem PELBTDUE Exmsnun :5 USED 77> use» amen 0F mist Two (PLURfiL IS EXTREnfi ) POINTS want we Dsmuanus Pix) :5 ElflrER 0 at? UNDEFINED n95 cmLED csmcm. POINTS Ex'rREnfi OCCUR fiT CRITICAL PowTS, Bur gr EVERY CRIT169L PmmT IS an Exmenun (SEE x: Q fiQOVE ) To DETEPnImE TIIE EXIREDI) we nusr WIPEFoIPE Do 7:00 mwss : L FIND TIIE cmncm. Powrs ( ConPUTE Pix) IIM) FIND our win-TE IT IS EIflIER 0 at? UNDEFINED) z- " rssr " sec» cmncm. Powr T0 oersnmms IF ms 19 RELM’IUE nfixmun, I9 IPELnnuE nmmun, oI? NEIIWER. Tfif FIRST OF THESE IS EHSY 0N0 wE’LL SEE DHN)’ EXfiflPLES SHORTLY, Fan ms sscomo, THEPE fiPE 7100 "1-5er " AvmweLE, 7715 FIRST 0F wHICH we HAVE PEIuLy ALREflDy usED' rumpus/J wE DIDN'T GIvE IT I9 IvfinE. Z’IE FIRST DEPIWITWE TEST! SuPPosE put) mes I9 cmrIan Powr I97 Xo (EIDIER Nata) :0 0)? P's: Ivor DEFINED I97 X0 ), 1F °——-'H X 0 l5 n~ INTERvfiL 17m cammms No 07715-7? cmncm. Powrs or: P, mm (a) o-——-——+————«= => P mas A REL/"TOE noxmun nr x0 °'—_“"—° => P HHS A Rename mmnun fir X0 Lb) X 0 P30 I F<o 0———I———o % 9 H95 msmmz n PELHTWE maxmun N02 0 PELnTwE nIIwnun 01' x0 cc) F'VO P'm sxnnPLEs: FDR sac” 0F rue Fouowwc Fumcnoms Pun FIND nu. 0F THE cnmcm. POINTS am) 01.05:!” EACH as a PELMWE nnxmun, PEMTME DINMDI), 0R NEITHER. 5' -— :1 l. Fax) : 313-15x’ I cmncm. POINTS : Put): 5x 3. 3 —mx .1. ~: = 5x Lx-m 50"3) J- x3 H WHICH IS 0 quN X = .2 MW) UNDEFINED quvu x: o O I I a l 9’0 F<a ¢>o Rename «sumo: rmxmun mmnun .1. Fax): x3-3xz+73x-I canan POINTS : Fix) = 3x7-bx-i3 = 30:1. 3.x“) = 3Lx-I)" wmcH IS DEFINED EVERywHERE £100 0 wHEN X: I, 3. In x pcx) = x CRman Powrs : NOTE : Donfiw 15 X > o , x(-,‘,-)-unx)<u _ ,_:,,x F‘X) = x2- - x1. wmcu IS mwnys DEFINED (on: x >0) fimo IS 0 was» l-Jazx = 0 l-lnX =0 lnX =' ch)! = e' X = C o-———o——-—-—- 0 e CHECK THE 515» OF Fix) A; -I .u : "hue ) x: é:e Ip(é = (4.)?- e l+' : >0 ugh" -1 ‘) X: 81 PRC" = l 2‘: (8) - 1-2 - ———eq ‘0 o——-———o———— o 3 $3.50 FQO RELRTIUE nnxmun sonETmES THERE IS Hm EBSIER way To " 7531 " fl cmnan Powr, I Surpass Fax, ) = o (n Powr wIiE/PE Tiff BERN/97705 :s 0 as sons'rmss CBLLED n smnonfiw Powr ), THEN II A F exp) < 0 => Comcmmy IS Datum 07 X0 —.__ =» RELnnuE nfixmun m x0 x0 V F'on) y o # cowcnvny :5 UP M X, ——-——— : RELnnve nwmun HT X0 X nowevE/r, IF P'Exo) = o mam momma can BE comcwoeo 33001 THE warms 0F rue cmmm. Pam‘r, 1. E. , :1 man BE A nmmun (E. 6., Put) = xv 191' x°=o ), .9 nfixmun (E. 6'.’ PM): -x" nr XO= 0 ), 0R NElflfER (Ea, Fun-”(3 In X,=O). Lug sscomo osmmnus TEST : IF 92x0) = 0, m5» I. Nab) us © RELnTIUE 171910000 #7 X0 4. F"cx,) > a ==> RELATIVE nwmun AT x0 3. F'Zxono =§ NOTHING crsermLs! ) sxflnPLES : Fol? EACH OF THE FaLLawwe Fvwcnoms 9.x) FIND BLL 0F THE CRITIcaL POINTS fiND CLBSSIFy EACH 05 B RELflTwE nexmun ) REL/977W? nwmunpk NEImER. I. PM) = x3- 3x43~ F'cx) = 3xz-3 = 30:14) = 3(x-:)cx+;) wmcu ls DEFINED EVERywfiEkE 0M) 0 m- x = -I am: X: 1, Fun!) = 6): WM) 2 -c < a => RELHTIVE nfixmvn m x: -I Put!) = 6 >0 : Psmnusnuwnunar x: I 2. FOO: ix-SINX 0N O‘X‘Qn’ II Fan = SINX .. (3' 9 L 3'35) = Sm at = '3: ’ 0 § RELnTIvE nnwnun 191’ X: I 3 ll Sn- ” r3- ? (—3-): SIN-5- =--;_- <0 é REL/mos nfixmon . £1- 81 x' 3 I NOTE : J'F emu-‘1? I“ vs UNDEFINED 07 x0 93 13 1x0) = a, me» 7715 SECOND DERIVB'nuE TEST IS OF NO USE. USE THE FIRST DEPmnnoE TEST nosTEAD, /= pix ) A iwrm‘menmwmmum x SKETCmNG THE GIMP” 0F )1 : Fax) : 1. FIND flu. Pawns HT wmc u THE BEHAVMR OF THE GIMP)? coULD mamas , (M Powrs NOT 1» m5 Dani-MN 0F ‘3 : Put) UNDEFINED a.) POSSIBLE EmenE POINTS : P'cx) 2520 at? omostz-‘D to P05 $133.5 INFLEC mm POINTS : fix) 25110 OR aonI-‘wso 2. THE X - COORDINMES OF THE POINTS mm ”1 DIVIDE m5 x-fixu UP mro INTEPanS ON wI-ucy THE 35;”;va CBNNOT' CIMNGE, 1. E. J on) wmcn Tle 6mm IS ONE OF 1716 FoLLowwc TYPES : I I; (a) P ’ 0 3ND ’2 5 0 : J Lb) F, > 0 am: F < 0 " /' u.) F'co mm Fu>0 3 \_ \ a u . (J, 9‘0 fiND F‘O ' 0575!?"le TUE 31cm 0F [3 AND P "am 59c» wrath/19L 3y CHECKING ONE POINT w sac». PIECE THESE cquEs TOGETHER, BEING CfiPEFUL To wow/9173 3, «mm NECESSfiRy (am) FEBSIBLE ) nDD tNTE/PCEPE 06:0 am: y = o ) mo umzoumz. nsynpmnes c lm Fm) x->t°° EXflnPLES : ., 3 l. y = Fax) = x - .2x comma» EVERYWHERE ) = X31304) (x-INTERcEPK HT x=oJ x=a.) F'cx) = 4x3— 6 x?" L DEFINED EVERermRE J = 2x1 Lax -3 ) I 3 Fm=o er x=o mm x=~g y- cooflolmfin's : Pm) = 0 .2'7 3 _- .._- Hz)’ lb '7 M” £%a*?z) Mo = lthux commas EVERYwHERE ) = (aux-1) F'Zx) =0 fiT x=o n~o x=I y - caotwwnn-‘s : Pm = a fi (I) = --l (0,0) Lu") Mmemwmm: .. “WWWWM w .. memwvw w...“ M.» x (0,0) (4,0 ) a 32 mn..n... ’6 WWW—‘4 _ _...’.- ....n,. Emmi”. "K...“ -m a” J .n. n A. m. o l .3- : l , a I F ‘ 0 F ‘0 P ¢ 0 F > a I " H F" ’0 9,0 F )0 I! )0 kW\ J Now mace rm-‘se racer-um J, norms mm maps me No HomzommL HSVanTES L Im (x"-.zx’) = °° ) nun) mar THE 62m» xatw ’ .17 PBSSES THROUGH (0,0) mm (33-, - 7; ) HomzonLLy. 7 firm = x1178 xi“ = pt) : Y " x"~) - ‘IX PICK) : """""'"‘ “"41" FI’X} “33340 L : (xi-U3 VERTMOL asynpmrs UNDEFINED 37 x = '1 mun x: I NEVER 0 50 NO 7: ~ INTERCEPTS. z .1. hn x.“ = Inn .1. = I x42” :91” I- xt- so THERE IS 9 00212010729). asynprors er HEIGHT 1 w 8077; 01066770105. c CoanTE 77m youRS‘ELF ) DEFINED EvERywnEIeE (on moonaw 0F F ) Flax) = o 97 x: a (0,-1) c. conPUTE 171/5 YauRSELF ) DEFINED EVERfloHERE (on me Dormw or- p ) NEVER O. / vsmcm. asynpnrs \ : I t : Horas-mm. ! I I .0 | I I : : fiSYflPTbTE I Q I 1 I0 w...— M a m my¢wmlwmr¢ mm mmmr»w .0-qmo..« mm ~l O I FIN) 930 P'<a F20 F">o 9'20 33"“ 9"» Y I 9 s V o 4 v I i 1 i i a i A f i E i 7 a I I I V ' I V I a (gm W x . n 0 I l t d d ! 9 I 6 1 4. a 3 3 = x tx +3) (DEFINED EVERYwHERE ) c x- mrEkcE-‘PTS m x = a, x = -—3 ) x + a = an v/3 C ConPUTE THIS YOURSELF ) X cx+3) F'tx)=o AT x: -I F'tx) UNDEFINED HT x=o fiND X: -3 I; 1.2. 3 y-coaRDWfiTES': PM) = « H PM) = 0 351-3) = 0 3 (":'V‘! ), (0,0), (—3,0) m NEVER o , F'lx) UNDEFINED m X: 0 mm x = -3 cnmenoy nave mess Pomrs D ‘I. ’3. y:?uu F'Lx) FutaU 'O -x xe U-x)e -x tx-J)C DEFINED E vsflywfiERE . Inn FIX) = 0 . "n X-"°° x-a-w HomwNTHL THNGENI A ;numsan~c x ‘I CONCAVE UP X> Z . INFLECDDM Pom” 9T Y ~nuTERCEPT AT X30 fix) =‘°° T (ué) oscnenswe x > I , Co~cfiv€ DDwN X < Z 2 t 4. a" ) ...
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