Section 14.6: Directional Derivatives & Gradient Vector

Show that the ellipsoid \(3x^2 + 2y^2 + z^2 = 9\) and the sphere \(x^2 + y^2 + z^2 - 8x - 6y - 8z + 24 = 0\) are tangent to each other at the point \((1, 1, 2)\). (This means that they have a common tangent plane at the point.)