Assignment 4: Applications of Differentiation (80 marks total) Your mark will be given as a percentage. [10 marks] (4 marks J (3 marks J (3 marks J [10 marks] (5 marks) (5 marks) [10 marks] (6 marks) (4 marks) [10 marks] (5 marks) (5 marks) 1. 2. 3. 4. For x) = 2x2 x4, a. Give the interval(s), in interval notation, on which f is increasing and on which f is decreasing. 13. Find and identify any relative extremes. c. Sketch the graph. For each function, give (and identify) any extrema and points of inection. Give the interval(s), in interval notation, on which f is increasing, decreasing, f is concave up and f is concave down. a. f(x) = x3 3;r2 +9x+ 12 41' b. g(x) = xe Find and identify any asymptotes (vertical, horizontal, or slant} or holes of: 314512 2x3+x2 a. x) = 20 b' 9(tj : 3+592t Find the absolute maximum and minimum values of each function over the indicated intervals. 4:: a. f(x) = over [3, 3] x2+1 b. g{x] = ln{:l:2 + 4) over [3, 1] [12 marks] [8 marks] (4 marks) (4 marks) [10 marks] [10 marks] (5 marks) (5 marks) 5. 7. 8. A rectangular box with a square base and a cover is to have a volume of 10 m3. [t 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, nd the cost of the cheapest such box. Use differentials to approximate of each of the following. Give your answer as a fraction. a. W b. $10001 (1' Find y using implicit differentiation for the curve: sf x22x3y2+5y+2=0. Suppose that the price, p, in dollars, and the number of items sold, x, are related by: p2 - xp + x2 = 175. . d a. Fmd p. d1: b. If p and x are functions of time, how fast is p changing with respect to time when p = $10 and x is increasing by 5 items per day