Q6. (a) Find the absolute maximum and minimum of f(x, y, z) = x - y + z subject to x2 + y' + z = 4 using the method of Lagrange multipliers. (b) Use CalcPlot3D to sketch x2 + y2 + z2 = 4 and well as the level surfaces of x - y + z which realize the the maximum and minimum. (c) This optimization problem concerns two very fundamental ge- ometric objects: planes and spheres. It is a very special prob- lem, because it admits a direct geometric solution. Explain how could you solve this problem by using properties of planes and spheres instead of the method of Lagrange multipliers