PART 1: CALCULUS [80 min] 1. Determine the derivative of the following functions. DO NOT SIMPLIFY . 5 marks b) f(x) = cos* (e-3) 2. Graph a function, g(x) that has all of the following properties below. [5AT] i. limg (x) = - ii lim g(x) = 3 ili lim g(x) = lim g(x) X-+0+ iv. lim g(x) = 1 V. lim g(x) = -13. Some of these four curves represent derivatives of one another. Fill in the table: [41] Function Derivative A Pair 1 B D Pair 2 For problem 4: [4 KATC] Define variables and draw a sketch [1] State the restrictions of the variable on your function [1] Develop the function to be optimized (objective function) [2] Optimization Problem (Your own problem here) Choice 1: Sandy is making a closed rectangular Choice 2. You participate in a biathlon jewelry box with a square base from two different involving swimming then running. The minimum woods. The wood for the top and bottom costs distance to swim across the river is 4 km. The $20/ma. The wood for the sides costs $30/m2. Find the dimensions that will minimize the cost of the maximum distance to run is 12 km. You swim at wood for a volume of 4000m3. 5 km/h and run at 7 km/h. At which point across the river should you swim towards such that you minimize your time? I choose5. Rates of Change Problems - 9 marks. Your position is given by the function, d(t) = $3 - 6+ + 9t + 1 where d is the distance from home and t is the hours since noon. Your travel starts at 12pm and ends at 4pm. Note: 0 s t $ 4 a. Determine the time(s) in the form of (HH:MM) where you are not moving. A3 b. Calculate the time intervals where you are speeding up. A3 c. Calculate the time(s) when you are the furthest from home from noon to four o'clock. A3