A surface S is defined by z -f(x, y) - a 6xy | 8y [7 Marks] i) Find the local maximum, the local minimum and the saddle point of the surface if exists. [7 Marks] ii) Estimate the value of z on S when x - 4.1, y - 1.9 using the approximation of tangent plane at (4, 2, 0)