Question

9.6 Maximum and Minimum Values Find the local maximum, minimum, and saddle points of the following functions. f(x,y) = ycost f(x,y) - * (x2 - y2)

Answer 1

DiPFeraHate e oT equate to ceao we fet 0) i on ly Critical point for fay) oT.t afdResp oeget Piff e 1 y cos O ny Consides 0 O-I -I 1 frn(E0) DC72,0) 20 20 ) is Saddie poist for P)ycosn

DIfferectiate e fequate to 2ero YY (Yy)e neo2 EY20 ty 203 0,0), C-2I0) Critical points are Tan=Ca ane Fam (o10)2 -2 2e +, , - - 1 <ל yCe70)2 fyy (-2,0):-2e (210)= tay -2ye Ty (o,0) 0 Connder D(o0) Fn a) - (ay o) (010) - 2 (-2) - O-4 DC010)0 l0cal minimum at Co0) has LThe funchon 2 A 62 4 e o and Fum 2,0)0 D (-210)0 local maximuM at -210) function has The

by second derivative test which mentioned in image i was solved this problem

Function., aud T(b) -0 ,y(ab)a be a 1et try) 1 Revet Draib)(ab) yyCa)-() with then Caib) local maximun. FD(a,b)> tm(a b)o it Dla.b)0 (ab)o Caib) is oce mnimum. (9(b) Sadtle perint D(aib)0 then then Test Failc CA D(anb) o