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Question 4 Below is a graph representing part of the cross-section of Mount Tango. The y-axis represents the vertical height (in metres), above the base of the mountain. The x-axis represents the horizontal distance (in metres) from the origin. Mount Tango y 100 f(0, 80 ) 80 60 A ( 400, 40 ) 40 20 ( 800,0) >X 200 400 600 800 -20 -40- a) Find a cubic function f(x) to represent the graph above (A is the point of inflection). Include an appropriate domain. b) Find the gradient function f '(x). Question 4 continues on the next page...
Question 4 continued... c) Sketch by hand the graph of f '(x) on your own paper. You may use the grid below as a guide. Clearly label all key points. X (0,0) d) Using your sketch, find the steepest gradient. Thus, if a ski run is constructed on Mount Tango, state the most appropriate run classification (Beginner, Intermediate, or Expert). e) The cross-section pictured in part a) is just one-half of the mountain. The left-hand side of the mountain, given as function g(x), can be found by reflecting the function f(x) in the y-axis. Give the equation for g(x). f) Looking at the functions g(x) and f(x), state the limitations of using these functions to model the side of a mountain. What assumptions have been made that may affect the reasonableness of your solutions? Page 9 of 13