I am trying to find the maximum or minimum for the following function with a constrain.
f(x,y,z)=x^2+y^2+z^2 s.t. 3x^2+4y^2+z^2=12.
I set up a Lagrangian, however when I take my first order conditions. I only get that lambda must be equal to zero and all values are zero.
Should I set up a bordered hessian?