3: Applications of Differentiation (80 marks total) Your mark will be given as a percentage. [10 marks] (3 marks) For () = 2 2 4 , (3 marks) b. Sketch the graph. (4 marks) c. Give the interval(s), in interval notation, on which is increasing and on which is decreasing. [10 marks] 1. a. Find and identify any relative extremes. 2. (5 marks) a. () = 3 + 3 2 4. (5 marks) [10 marks] b. () = 4 + 4 3 3. (5 marks) 4 4 5 2 3 +2 2 3 b. () = 31 . 4. (5 marks) . Find the absolute maximum and minimum values of each function over the indicated intervals. a. () = 4 8 2 + 3 over [-3,3]. 2 (5 marks) [12 marks] Find and identify any asymptotes (vertical, horizontal, or slant) or holes of: a. () = (5 marks) [10 marks] For each function, give (and identify) any extrema and points of inflection. Give the interval(s), in interval notation, on which is increasing, decreasing, is concave up and is concave down. b. () = ( + 3)3 1 over [-4,5]. 5. A rectangular box with a square base and a cover is to have a volume of 10 m3. If the cost of the material for the top and base is $10 per square metre and the cost of the material for the sides is $6 per square metre, find the cost of the cheapest such box. [8 marks] (4 marks) 6. Use differentials to approximate of each of the following. Give your answer as a fraction. 4 a. 82 , using implicit differentiation for the curve: 2 2 3 2 + 5 + 2 = 0. [10 marks] 8. Suppose that the price, , in dollars, and the number of items sold,, are related by: 2 + 2 = 175. (5 marks) . b. If and are functions of time, how fast is changing with respect to time when = $10 and is increasing by 5 items per day