Question

61. (14.8) Find the extreme values for the function 8y - 4x subject to the constraints y2 + x2 – 1 = 0 and 2x – 2 - Y - 2 = 0.

Answer 1

Given - function, sy- ux the fenction is seobject to constraints yux-1=0 22.9-3-2=0 f(o4, 2) - 8y-48 de=-; dy - 8 ; do glany, 2) = x'ty-1=0 => gost 2x ; gydy:9220 hlay, 3) = 2X-4-3-250 = e = 2: hy = -1;hga By using lagrange multiplier we can write fe = dgx + he ha -o glary, 2) = x²tyta dy = agy tehy - h (214,8) = ax-4-3-220 da = dgg telha - f(x,y, 8) =-48484 Now pead the values in the above eg's 0.0. - 4 = X(2x) + 4 (2) o=2(0)+ 4 (al) 8 = $(24) + le cou) Fil=0] u=o then 4²+ (2x) 4 = x (29)

lifrin = -415 - Amace = urg .The Extreme values of the gives function is Spon-- Chem p i Y5 - - - ()--(2-)«( SARL : P ŞI =* uogh SNC-=Y 42 In = (gemet p: GA SA (94-)«n- en