Find a normal vector to the level surface of f(x,y,z)=x2+y2+2z2f(x,y,z) = x^2 + y^2 + 2z^2f(x,y,z)=x2+y2+2z2 at the point (1,2,1)(1, 2, 1)(1,2,1).
⟨1,2,1⟩\langle 1, 2, 1 \rangle⟨1,2,1⟩
⟨2,4,4⟩\langle 2, 4, 4 \rangle⟨2,4,4⟩
⟨1,2,2⟩\langle 1, 2, 2 \rangle⟨1,2,2⟩
⟨2,4,2⟩\langle 2, 4, 2 \rangle⟨2,4,2⟩