Answer Happy

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 (0,80) (800, 0) 100 80 60 A (400, 40) 40 20 200 400 600 800 -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).
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. y 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?