the derivate of x^2 + In (x^2) =? 1.O 2x-2/x 2.O 2x^2 +2/x 3. O none of the other answers 4. O 2x +2/x 5. O 2x+1/x^2 A multiple-choice question with one possible answer. (Required) the second derivate of 1/x+ exp(x) =? 1.O 1/x^3+ exp(x) 2.O-1/x^3+ exp(x) 3. O 2/x^3+ 2exp(x) 4. O 2/x^3+ exp(x) 5.O-2/x^3+ exp(x) A multiple-choice question with one possible answer. (Required) The following function at x=4 is y=3x^2-14x+5 1. O decreasing 2. O increasing 3. O uncertain 4. O stationary A multiple-choice question with one possible answer. (Required) Consider function: f = 3x^3-9xy + 3y^3 1. f has a relative maximum point at (x, y) = (1,1) and a reflection point at (x, y) = (0,0) 2. f has a relative minimum point at (x, y) = (1,1) and a maximum point at (x, y) = (0,0) 3. f has two stationary points at (x, y) = (1,2) and (x, y) = (0,0) 4. f has a relative minimum point at (x, y) = (1,1) and a reflection point at (x, y) = (0,0) relative maximum point at (x, y) = (1,1) and a minimum point at (x, y) = (0,0) 5. f has a A multiple-choice question with one possible answer. (Required) for the following demand function of the monopolist, P = 2 - Q; if the marginal cost is zero, then the optimal output level is: 1.0 1 2.0 8 3. O 2 4. O None of the other answers 5.0 -1 A multiple-choice question with one possible answer. (Required) Use Lagrange multipliers to optimize the following equation subject to the given constraint: z = 4x^2-2xy + 6y^2 subject to: x+y=72 1.0 (x, y) (42, 30) 2.0 (x, y) (20, 52) 3. O None of the other answers 4. O (x, y) (32, 40) 5.0 (x, y) (37, 35) A multiple-choice question with one possible answer. (Required) A firm producing goods x and y has the following profit function: z = 64x-2x^2+4xy - 4 y^2 + 32 y - 14 Its production capacity is subject to: x+y=79 ( The inverse of the following matrix is 7 9 6 12 1. O -2/5 3/16 -1/5 7/30 2.0 -2/5 3/16 1/5 -7/30 3. O 2/5 -3/16 -1/5 7/30 4.O 1 0 1 1 A multiple-choice question with one possible answer. (Required) Calculate AB for the following two matrices A and B: A= 7 11 2 9 10 6 B= 12 4 5 3 6 1 1. O AB= 117 94 45 51 62 18 138 76 56 2. O AB= 117 94 45 51 61 19 138 76 56 Choice 1 3. None of the other answers 4.O AB= 117 94 45 51 62 19 138 75 56 5. O AB= 117 94 45 51 62 19 138 76 56 A multiple-choice question with one possible answer. (Required) The determinant of the following matrix is 2 6 -1 5 1. O 4 2.0 11 3. O 26 4.0 16 5.0 2