[12 marks] 1. For f (x) = x6 - 3x2 (3 marks) a. Give in interval notation the intervals where fis increasing and where f is decreasing. (3 marks) b. Give in interval notation the intervals where fis concave up and where f is concave down. (3 marks) c. Give the coordinates of any points of inflection. (3 marks) d. Sketch the curve. [12 marks] 2. Repeat question 1 above for f (x) = e-x2 [10 marks] 3. A wire 10 m long is to be cut in two pieces. One piece is bent into a square and the other into a circle. How should the wire be cut so that the total area enclosed is (5 marks) a. a maximum? (5 marks) b. a minimum? Give exact answers and then to one decimal place. [10 marks] 4. A boat leaves a dock at 2:00 pm and travels south at a speed of 20 km/h. Another boat has been heading east at 15 km/h and reaches the same dock at 3:00 pm. At what time were the two boats closest together