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)