The sphere 2+ y+z = 36 and the plane x + y + z = -10 intersect in an ellipse. Use Lagrange multipliers, or any other method, to find the lowest point (= point with minimal z-value) on this ellipse. QUESTION 2 Find the absolute maximum and absolute minimum values of the function f(x, y) = (x-1)+y-3y on the region {(x, y) = R : (x 1) + (y-1) 9}. Hint: to find the maximum and minimum on the boundary of this region, you might want to use Lagrange multipliers. QUESTION 3 Find the absolute maximum and absolute minimum values of the function f(x, y) = x + y + z on the region {(x, y, z) = R : x + y + z