1. At what point is the following function a local minimum? {image}
(-1, 15)
(0, 0)
(1, 15)
(-1, 10) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. At what point is the following function a local minimum? {image}
(6, 9)
(9, 0)
(6, 0)
(0, 0) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. Find the critical points of the function. {image}
(4, 0) ,(-6 ,0), (2, 0)
(4, 0) ,(6 ,0), (2, 0)
(4, 0) ,(-6 ,0)
(-4, 0) ,(-6 ,0), (-2, 0) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. Find the absolute minimum value of the function f on the set D
Find the absolute minimum value of the function f on the set D. D is the region bounded by the parabola {image} and the line y = 4. {image}
-45
-52
-49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. Find the dimensions of the rectangular box with largest volume if the total surface area is given as 216 {image}
24 cm, 1.5 cm, 1.5 cm
12 cm, 12 cm, 3 cm
216 cm, 6 cm, 6 cm
6 cm, 6 cm, 6 cm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50