(1 point) A closed rectangular box with faces parallel to the coordinate planes has one bottom corner at the origin and the opposite top corner in the first octant on the plane 4x + By + z = 1. What is the maximum volume of such a box? volume = (1 point) Does the function 2 f(x,y)= x3+2y3 +9y2 2x have a global maximum and global minimum? If it does, identify the value of the maximum and minimum. If it does not, be sure that you are able to explain why. Global maximum? (Enter the value of the global maximum, or none if there is no global maximum.) Global minimum? (Enter the value of the global minimum, or none if there is no global minimum.) (1 point) Let f(x,y) = 1 + x2 cos(3y). Find all critical points and classify them as local maxima, local minima, saddle points, or none of these. critical points: {give your points as a comma separated list of (x, y) coordinates. if your answer includes points that occur at a sequence of values, e.g., at every odd integer; or at any constant multiple of another value, use m for any non-zero even integer, n for any non-zero odd integer, and/or k for other arbitrary constants.) classifications: {give your answers in a comma separated list, specifying maximum, minimum, saddle point, or none for each, in the same order as you entered your critical points)