At what point is the following function a local minimum? {image}

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Presentation transcript:

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

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

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

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

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