Question

55-56 Find the absolute maximum and minimum values of f or the set D. n 55. f(x, y) 4xxy2- x2y2-xy'; D is the closed triangular region in the xy-plane with vertices (0, 0), (0, 6), and (6, 0) x 2y2 ); D is the disk x2 + y2< 4 56. f(x, y) = e

both number 55 and 56

Answer 1

Ri crs We clord tuanyle t(x,9)4y D iD ( win vetices (o,0), (o, 6) amd 6, o) in xy-blane 4- 2xy 2 ) ty= 3xy2 b, o X Far eteme values ut fn=o, 1y = o y2 (4-2 y a 2n-1 = 0 as 4 2 - y 21 4 2 and (8-2 n 3Y = 0 ニ0 &-2n3 2x t 3y

2え +1 = 4 2nt3y=8 ox-2y- 4 ,we get in 2ung an ey 4 2え + 2=4 2x ニ 4-2 li es in tuianyle boint Ci, which to (0,6) Lo,0) 6, 0) Now at 2 os 2 の,we get 4 So paint (&o) and at Y=On S 2 & =) r 4 , we set So point 4,0) fom 4. we set uning Ox+ y4 point is (0,4J and at in (6 we x o j-8/s So point in Co, 813) 4,0), (2, ), (o, 81) (0, 4) E D So (4,0 =o 7(0,81) /(0,4) and t,2 = = 16-4-8=4 manin umm valu t al (,2) 4 i absoute f(o, 4)- minimum valu at (0,0), (2,0),4,02(, 9),,1) l0,0)-t90)( 9,0) = flo, 8s )