Find all local maxima, local minima, and saddle points of the given function for 27 and 28, and for 29-32 answer accordingly 27. f (x, y) = x2 ? 2xy + y3 - y 28. f(x, y) = 3x 2+ 6xy + 2y3+ 12x? 24y 29. find the absolute maxima and minima of the function f (x, y) = x2 + y2 - 2x on the triangular region with vertices (0, 0), (2, 0), and (0, 2). 30. find the maximum and minimum values-if any - of the function f (x, y, z) = x2y2z2 subject to the constraint x2+ 4y2 + 9z2 = 27. 31. find the maximum and minimum values - if any - of the function f(x, y, z) = z subject to the constraints x + y + z = 1 and x2 + y2 =1. 32. find the point on the sphere with center (1, 2, 3) and radius 6 that are closest and farthest from the origin.