Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid (Z32 y2 22 _ _ _ : 1 36 + 9 + 49 Hint: By symmetry, you can restrict your attention to the first octant (where at, y, z 2 0), and assume your volume has the form V = 8:1:yz. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the rst octant. Maximum volume: (1 point) Find three positive real numbers whose sum is 4 and whose product is a maximum. Enter the three numbers separated by commas: Find the maximum and minimum values of the function f(a:, y, z) = yz | my subject to the constraints y2 | 22 = 361 and my 2 6. Maximum value is . Minimum value is Find the maximum and minimum values of the function at, y, z) : $2y222 subject to the constraint m2 + 3/2 i Z2 = 324. Maximum value is , occuring at points (positive integer or "innitely many"). Minimum value is , occuring at points (positive integer or "innitely many")