I am trying to solve this question using lagrange multipliers. pls help me see if i am doing it correctly.

$$f(x,y,z)=x^2+y^2+z^2$$
$$g(x,y,z)=xyz=1$$

$$f\_x=\lambda g\_x=2x=(yz)\lambda$$
$$f\_y=\lambda g\_y=2y=(xz)\lambda$$
$$f\_z=\lambda g\_z=2z=(xy)\lambda$$

i obtained 4 points here I would like to know if the points i have obtained are correct or are there more to it? Also is this a min or max since they are all the same?
$$f(1,1,1)=3$$
$$f(1-,1,-1)=3$$
$$f(-1,1,-1)=3$$
$$f(-1,-1,1)=3$$