Answer Happy

13 of 14 Question 6 "Penta Ski Resort" plans to make the fifth mountain, Mount Fairweather, the main mountain. It will have three runs, one for each type of skier (Beginner, Intermediate and Expert). This will require a chairlift for each run. a) Surveyors have determined the best function to represent the cross-section of Mount Fairweather is y = 0.05 x? e(-0.01x), where 0 < x < 1000, where y is the vertical height (in metres), above the base of the mountain and x is the horizontal distance (in metres) from the origin. With the help of your calculator (Hint: set a correct Window for your calculator first), graph the cross- section of Mount Fairweather on your own paper. You may use the grid below as a guide. Clearly label coordinates of the endpoints and the turning point. 300 250 200 150 100 50 ol 100 200 300 400 500 600 700 800 900 1000 X b) Use the product rule to find the derivative y'. Give your answer in fully factorized form. Question 6 continues on the next page... Page 12 of 13
14 OT 14 Question 6 continued ... c) Hence find the x-value of the local maximum. d) Consider the graph of the derivative function (y') and the labelled points, shown below: (2000) 100 300 400 500 600 700 000 RO 1000 (564348-0.364) (416,584 -0.7) These points can be used to find the best positions for the chairlifts for an Expert run, Intermediate run and Beginner run respectively, so that each type of skier on Mount Fairweather will have the longest run possible. Plot Points A, B, and C on the y graph in part a to represent the best positions for chairlifts for an expert run, intermediate run, and beginner ski run, respectively. The points should represent the longest run possible as shown in part d. (Round coordinates correct to 3 decimal places.) End of Group Task Page 13 of 13