Let S be the surface xyz = 1 in the first octant. Let P(x0, y0, z0) be a point on S (so x0, y0, z0 are all > 0). (a) Find the equation of the tangent plane to S at P. (b) Draw the tetrahedron bounded by this tangent plane and the planes x = 0, y = 0, and z = 0. Then work out the volume of the tetrahedron. Show that the volume of this tetrahedron will always be 9/2, regardless of the choice of the point P on S (since x₀y₀z₀ = 1.)