Dear all
I solve an optimization problem ( minimization or maximization) using lagrangeMultiplier theorem
The objective function is f:=(x,y,z) =x*y+y*z;
The constraints are: x*y=1 and y^2+z^2=1;
Using a numerical method I get the follwing point
x = 1.41421356249703, y = .707106781124551, z = .707106781248575
How can I confirm that this point is a minumum or maximum
Maybe I must use Hessian matrix or something else.
Which condition must be introduced to know the type ( maximum or minumum) this point.
Many thanks for your help