A25.1 (5 marks) By calculating V x V, show that yz2 + 3 V(x, y, z ) = 22+2z+1 2xyz + 2y can be expressed as V = Vo for some function o, and find o. A25.2 (5 marks) We wish to find the greatest and least values of f(x, y, z) = xy - xz on the sphere x2 + y2 + 22 = 1. (i) Write down the Lagrange multiplier equation. (ii) By solving the Lagrange multiplier equation, find the maximum and minimum of f on the sphere, and the points where these values occur