EDB — 1Q2

[1Q2]Given \(m{\gt}0\), show that the relation \(xyz=m^ 3\) defines a surface in \(ℝ^ 3\). Prove that the planes tangent to the surface at the points of the first octant \(\{ x{\gt}0,y{\gt}0,z{\gt}0\} \) form with the coordinate planes of \(ℝ^ 3\) a tetrahedron of constant volume.