Answer all please

1. Find the maximum and minimum values of the given functions over each of the given intervals or explain why they do not exist. a. f(x) = 2x3- 3x- - 12x + 5 on the intervals i. [-3, 4] ii. [-1, 3] iii. [-2, 4] b. f(a) = 2 - 3x + 1 on the intervals i. [0, 2] ii. [-3, 2] c. f(ac) = as on the intervals i. [1, 8] ii. [-8, 8] 32-2 d. f(ac) = on the intervals x - 3 i. [-2, 2] ii. [2, 8]2. The number of salmon swimming upstream to spawn. N. is approximated by thefunction Nu} = t3 + 3:2 + 804: + 5000 6 3' t '3' 20. where: represents the temperature of the water in degrees Celsius. Determine the optimal temperature to maximize the size of the salmon population. 3. Athree-sided fence is to be built next to a straight section of river. which forms the fourth side of a rectangular region, as shown in the diagram below. The enclosed area is to equal 1800 m2 and the fence running parallel to the river must be set back at least 20 m from the river. Determine the minimum perimeter of such an enclosure and the dimensions of the corresponding enclosure. 4. A two-pen corral is to be built. The outline of the corral forms two identical adjoining rectangles, as shown in the diagram below. If there is 120 m of fencing available and the fence width cannot be less than 6 m, what dimensions of the corral will maximize the enclosed area? WIDTH5. An open rectangular box is to be made by cutting four equal squares from each corner of a 12 cm by 12 cm piece of metal and then folding up the sides (sample diagram shown below). The finished box must be at least 1.5 cm deep, but not deeper than 3 cm. What are the dimensions of the finished box if the volume is to be maximized? 12 cm 6. A rectangular picnic area of 8000 m is being constructed by the Parks Commission along the edge of a river. It will be fenced on three sides, but not along the river. Ornamental fencing costing $12/m will be used on the side opposite the river and chain-link fencing costing $3/m will be used on the other two sides. a. If the Parks Commission wants to have at least 40 m of riverfront, what are the dimensions of the picnic area that will minimize the cost of the project? b. If the Parks Commission wants to have at least 80 m of riverfront, what are the dimensions of the picnic area that will minimize the cost of the project