Question

Problem 6. to the cons o rernede (17 points) Find the absolute maximum and minimum of the function tained at Note: You can eam partial credit on the problem 1 Jump to Problem 2 Grade Test

Answer 1

By the method of legronge. Multiplier, Meximize/Minimise flery) Subject to g(x, y) = 0 2(x, y) of losy) - 2g(x,y) » Lex,y) = (x + y ²) - 2 (x + y - 1) 24 - 2x - 2[42) =0 .com ad 2y - 2 (443) = 0 . . (2) of x² + y4 - 1 = 0 ... (3) From equations a '2x - 214x3) = 0 = = x(1-22x2) = 0 2=0 or 1- 21x²=0 = x 2 = 1 um From %= II is vää u equation (22 _ _ 24 - 264 3) =0 : > y =o or 1-224 ²=0 TE 2012-0 o 22 = */ S Scanned with CamScanner

from equetón (32 +y" = Pluggino"x=0,4 =0 does not behifejthe "O equotón Plugging x = 0, y = 42² = 1 222 = 2 = 1 Plugging 2 = 1, y =0 2 » 42²=1 = 2 = Il Since .2270 for a/22 to exist - 2=+) 2 > x=0,7=0,(repected) x=0, y = 8/9 x = 1, y =0 _Phai * * * to the che *****hon CGU CS Scanned with anscanner 222-

اور * ht درود Calculating for. y) = x² + y2 - - - = 2 *(ر) + (ن) = ( ها (ر) = (و رم - - Therefore, Absolute maxima Eva occurs of ਆਜਾ ਆਵੈ ॥ Absolute minime = { occuricet ه ره را له CSScanned with CamScanner CS$canned with CamScanner