1. The problem statement, all variables and given/known data Find the points on the surface: z²-xy=1 nearest to the origin 2. Relevant equations grad(f)= lambda grad(g) (?) f(x,y,z)=z²-xy (?) g=(0,0,0) (?) 3. The attempt at a solution grad(f)=(-y, -x, 2z)= lambda (0,0,0) = (0,0,0) -y=0 => y=0 -x=0 => x=0 2z=0 => z=0 But (x,y,z)=(0,0,0) doesn't satisfy f(0,0,0)=1.