Hi

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.

dL/dx=2x+3lx=0

dL/dy=2y+8ly=0

dL/dz=2z+2lz=0

Should I set up a bordered hessian?

Thanks