Question

(5) Use Lagrange Multipliers to varify the minimize and maximum of f(x,y) = x+y x2 + y2 = 1 as found in the image below. (V2/2, 2/2, V2 if 1.82 12,- V 212, .V2X

Answer 1

solution fin,y)=nty fn = derivative of finiy) with respect of a fx=t fy= derivative of feny) with respect of y fyt using dangrange multiplier T fin, y, z) =.d. Tg (2,9, 2) Let gen,y)= n²4y2-1 gn=an gy=zy using Langrange multiplier t=ada - t=2ay - ③ 744251 - fremgant and you plug these two valles in e - 2 + ( ) ? =) Tu mane + t 2 = 21

3) 2071 22 d2=/ 2) d = 1 it d=-- Na ta n = {xc-ra) n=- Ž y = -1/2 if a=to sustaiga te minimum) Y muy Determine value of fengs on these two points f(-/-/17/2) = -1/2 1/2 = -2 = -126 f(t2, f) = 1/2 + 1/4 = 2 4 = vz (maximums f (x f(thi ) = -V2 Minimum ) = f maximary Answer.