PLEASE ANSWER ALL THE QUESTIONS.

Assignment 5 is graded with a total of 100 marks and it contributes 10 percent towards your course grade. [12 marks] (3 marks) (3 marks) (3 marks) (3 marks) [12 marks] [10 marks] (5 marks) (5 marks) [10 marks] 1. For f(x) = x5 3x2 a. Give in interval notation the intervals where f is increasing and where f is decreasing. b. Give in interval notation the intervals where f is concave up and where f is concave down. c. Give the coordinates of any points of inection. d. Sketch the curve. 2 2. Repeat question 1 above for f (x) = 8\" 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 a. a maximum? b. a minimum? Give exact answers and then to one decimal place. 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? [10 marks] 5. Consider the cost function, C(x) = 25000 + 100x + 0.1x2 where C is given in dollars. The average cost is given by c(x) = (3 marks) a. Find the cost, average cost, and marginal cost at a production level of 100 units. (5 marks) b. Find the production level that will minimize the average cost. (2 marks) c. Find the minimum average cost. [10 marks] 6. Use Newton's method to approximate the root of x* + x - 4 = 0 in the interval [1,2] correct to six decimal places. [10 marks] 7. Use Newton's method to find the positive root of 3 sin x = x correct to six decimal places. [8 marks] 8. Find fif f" (t) = e2t - 4 cost if f(0) = = and f ( ) = 0 [8 marks] 9. Find a function f such that f'(x) = x5 + 20 and the line 12x + y = -20 is tangent to the graph of f. [10 marks] 10. A car braked with constant deceleration of 5 m/s2 producing skid marks measuring 60 m before coming to stop. How fast was the car travelling when the brakes were first applied? Give your answer in km/h