1. Determine the absolute minimum and maximum of each function. given interval. (4 marks each, K)...

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1. Determine the absolute minimum and maximum of each function. given interval. (4 marks each, K) a) y=x+4x + x + 1, -1x5 2 80:26 2 b) y = x+ 0.5 x 5 x 2. Given the function y = x + 4x- 2x - 12x+9. a. Determine its domain, range, x- and y-intercepts. (4 marks, A) b. Determine critical numbers, local maxima and minima, and the intervals where the function is increasing and where it is decreasing. Explain your solution. (4/4 marks, A/C) c. Determine points of inflection, and where the graph is concave up and where it is concave down. (4 marks, A) d. Sketch the graph. (2 marks, C) 3. A farmer wants to fence a rectangular field the area of which is 200,000 m. He plans to divide the field in half with a fence parallel to one of the sides of the rectangle. Determine the dimensions of the field that minimize the cost of the fence. (5 marks, A) 4. A metal cylindrical container with an open top is to hold 25 m of water. If there is no waste in construction, find the cylinder dimensions that require the least amount of material. (5 marks, T) 1. Determine the absolute minimum and maximum of each function. given interval. (4 marks each, K) a) y=x+4x + x + 1, -1x5 2 80:26 2 b) y = x+ 0.5 x 5 x 2. Given the function y = x + 4x- 2x - 12x+9. a. Determine its domain, range, x- and y-intercepts. (4 marks, A) b. Determine critical numbers, local maxima and minima, and the intervals where the function is increasing and where it is decreasing. Explain your solution. (4/4 marks, A/C) c. Determine points of inflection, and where the graph is concave up and where it is concave down. (4 marks, A) d. Sketch the graph. (2 marks, C) 3. A farmer wants to fence a rectangular field the area of which is 200,000 m. He plans to divide the field in half with a fence parallel to one of the sides of the rectangle. Determine the dimensions of the field that minimize the cost of the fence. (5 marks, A) 4. A metal cylindrical container with an open top is to hold 25 m of water. If there is no waste in construction, find the cylinder dimensions that require the least amount of material. (5 marks, T)