332 Problemdg o 2Xy o y o If 40 lays_winA4y2xy l x4yfxytIa 43914tax yr sof10,070 So criticalpoint15localminima

3.34 problems

finny A4y43ay

ddtx zxtzy o.dftyhfty43AYI zytza.no

trip WMIIM 2

dyz 2 dady 3 D 2232 49 520

Therefore tiny 15 a saddlepoint

335 fhhytx23aytbxzytby48dfmdhf.at3Yt5 o

nay ftp.TdfhhY7dy l2Y3H2 o

Miffy o Maquis dtIYfy 3

D Ft dating dfday2 12 9 24945 o

Ttblocalminimum

3.38 fexytstnlxkyydftff

axa.sc yydtId'yH aywshayycriticalpoint lamp win

dttfqk.wsx4y3 Hx2sTnlx4y7 dFldf 2.70offload

Ty 2loshfty7 4429 14243 2

dfftonsdady ttxysm.tk143 0

D 470 Cons15thelocalminimum3.3.10 ftp.mp ytxstny

dfntdfkgtny.MILtxwsy.lxnfI this ChasCaryl_ftp.HMII.tv

ntNldfqdfo.d4IfyH sTny x d2tdHy cosy

Newlin D 140

road D ko Allprintsaresaddlepoints

3.3.12 ftxiyi txyltxyH npy x

yzxty.dfmjYYzxy i.gs dftfiytkxz.my o

Ftry my 7 AH Yt Uil

hey 9 1 yet Hi 11

dtahhjd.dz n sy.dtIIIgb zx.dtYIaay ayamusesecondderivativetest

megetthDissaddlepointGillis saddlepoint

3.3.14 daxfnnyr YYYF.it yjadyfnnyi 9fofsYnTxyfywstxys o.tn ryI 10107

xwsixyko.xto.y.to 7 tx.EEntNdcEIsf.gitdf aiEInstn

ddfjy oxysintxyitzqzyayi xy ismaywsxy.FIMyp

1710107 1440 10,0115SaddlepointDIX.AMa1 o.seiondderwatwetestdoosnhwork

3.3.16fhhytIAyitxyth xytxAYHY.de2HytItY ddf

gx42xytlyftoxytto.x sy.my Norealsolutin I 1,1x42AytI o Ky lyay2ti o.L2y H I 1

dp 2y dd

y x dday 2xt2y

y yusesecondderivativetestwegetHinchDaresaddlepoints

3.318 ftmfiztAZYHEkyz.ladfthfffZI.sn o.dfH'dY'y zy kz wMd 2ZtkY0

Xoq2y4KZ o YoZeo vftkz o 2Z ky.ae ComoTsa criticalpoint2ztKY.co

computeall ftp.dtfxy.dd z andputthemintothematrix

1 2,92

weneedtothismatrixtopositive definite

4152 0 15224 2715722

3.3.24 dfqpzaxdtayw.datp spdfdyz o.dfidyy.ae Testfails DaoWeknowapparently AHE A o forgo maximum

ANTE H2o Cory minimum

A o ways saddlepours

3.3.30

Mt y5 24242242 V Ayz oxyljIyY5 2 XYtXztyZ

I Y l512oxy 2tittyZ S72xy

xty

d dady

12 2t SHY ZAYkxtmp2xcszxygo.caxtup52xys zxykxnyluy5my o

p Ealyby2M0Story y x

substitute f xintoD4 152917 24441 2A 5242 0

211152117 2X14AMtog toAZ

2 E yHY a 342nd2X Mf

criticalpoint Xy zThenweusesecondderivativetesttoshowthecriticalpointisthelocalmaximum