Question

Please help solve the second part

Find the relative maximum and minimum values. f(x,y) = x² + y2 - - 18xy Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The function has a relative maximum value of f(x,y)= at (x,y) = (Simplify your answers. Type exact answers. Type an ordered pair in the second answer box.) B. The function has no relative maximum value. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The function has a relative minimurn value of f(x,y)= at (x,y)= (Simplify your answers. Type exact answers. Type an ordered pair in the second answer box.) B. The function has no relative minimum value.

Answer 1

Given f(x,y) = x + y² igrey fx (ny) at 3x²-184 Ju af 182 2 2 fy Cosy) 34² - oy ours where The unonima (or) minima 아 아 2 O dr ay 2_18n=o and 3 x ² - By: 0 3y 2 - y2 = 6x - and 22. by 22 2) y 6 put y a un 2. 22 br 6 M 62 ao 1 36 M ہو 2D 6) ne ( 13 6² 0 36 -) 120,6 no g. 20 when and when x26 ug 31 26

Thus the vitical opoints ame 100) and 6,6) Now, we need to check which is monima / minim forex (x,y) - - TV8 bu fyy (ny) = "18 by (x,y) - 18 sto (my). fry lwy) 1,6 at (oo) (-18)? (Cu) (y) - (18) a culative DLO thus (0,0) is monimum, 110,0) = 0 at (6,6) (6u) (6y) - (-18) ? z a72 relative is thus (66) 2) Do / 2 216 minimum f 16,6)