I am given a 3 variable function: f ( x , y , z ) = cos ⁡ ( x y ) + cos ⁡ ( y z ) + cos ⁡ ( z x )How to do the Hessian matrix for a 3 variable function.

Question

I am given a   3 variable function:  f  (  x  ,  y  ,  z  )  =  cos  ⁡  (  x  y  )  +  cos  ⁡  (  y  z  )  +  cos  ⁡  (  z  x  )How to do the Hessian matrix for a   3 variable function.

Isabella Rocha · Accepted Answer

Notice that since   cos  ⁡  (  w  )  ≤  1, hence   f  (  x  ,  y  ,  z  )  ≤  3.Also note that   f  (  0  ,  0  ,  0  )  =  3, hence   (  0  ,  0  ,  0  ) must be a global maximum.No computation of hessian is needed.Remark:The hessian is the matrix       [                                        f                          x              x                                                            f                          x              y                                                            f                          x              z                                                                        f                          y              x                                                            f                          y              y                                                            f                          y              z                                                                        f                          z              x                                                            f                          z              y                                                            f                          z              z                                            ]

I am given a 3 variable function: f(x,y,z)=cos(xy)+cos(yz)+cos(zx) How to do the Hessian matrix for a 3 variable function.

Open question

Answer & Explanation

New Questions in Differential Calculus