Given f(x,y,z)=x3+y3+z3−3xyzf(x, y, z) = x^3 + y^3 + z^3 - 3xyzf(x,y,z)=x3+y3+z3−3xyz, what is the nature of the critical point at (1,1,1)(1, 1, 1)(1,1,1)?
Local maximum
Local minimum
Saddle point
Degenerate critical point