Question

Find the values of x, y and z that correspond to the critical point of the function: z = f(x, y) = 2x2 1x – 6y + 4y2 + 2xy Enter your answer as a decimal number, or a calculation (like 22/7) = X Preview (Round to 4 decimal places) YF Preview (Round to 4 decimal places) z Preview (Round to 4 decimal places)

Really need help with these problems, it would be really appreciated. Thank you!

Answer 1

Solh Giren = z = feny=28=12-6y thy Fixy un-1t2y Then əZ an = ze he -6t8y+z2 critical point are have For az aa 0 = joan zo. Hence, 4x+2y-1=0 2x+8y-6=0 Jolving , 17 = u + =hc 11 TY

36 thene i in o, we Putting get 2(-1/25 - 1(-21)-6(th) +4 (thy +265) Z = -116 49. n= ht ya 11 14 z = -116 49 Crear) @ Soh ze we Instead of minimizi zing the distance can m minimi the square of the distance ď = (2-35+ (y_45+ z since z==xityr the function to minimize in tea, y = (n-37+ (9-45% artyr derivatives Take the partial and set them equal to zero; tx=2 (2-3) + 2x = 0 ty=2(4-4)+2y =0 (x,y) = (², 2) in the only critical point giving the come Jolring the points

28 25 4 &, 2, 4) (2, 2,-2) (z%= neityn =12~= (25+2^= + z = = = hart, need to use tecond derivative to make sure thin minimun tna a, fay Jo, D= fox tyy (tong we a mi 02 = 4 szy = 4 = 16 so and from to point so there gire minimum distances. &, 2, 3); (22, 2, 4) (reag 3. 2 )