Question

Find all points where the function has any relative extrema or saddle points and identify the type of relative extremum. f(x,y) = x3 – 12xy + 8y3 A. Relative minimum at (2,1) and relative maximum at (0,0) OB. Relative minimum at (2,1) and saddle point at (0,0) OC. Saddle point at (2,1) D. Relative maximum at (1,2)

Answer 1

Dco (ay) saddle point Relative minimum at (211) & saddle Solution flary) = x² 12x4+84² for critical points faro, fy=0 fa-34?_12 y=0,14-121+244-0 for = bai fyge 489 , kay = 12 D= fan fyy (fray) 2 care D70, fax>0, (ny) is a minimum Dyo, fanco, (a) is a maximum this ① D=0, no statement can be made wing approch fx = 0 31²12y=0 #2y²=0 3 (2²-44)=0 & 1² - 44 x=24² solving critical points are 1010)8(2,1) for 1096) D- O-H2)2--14420 (saddle point) (212 D- 12148) - (2)? = 432 >o (minimum point at 10 10,0)