Chapter 7.6, Problem 19MS

Too high. Consider a tent function that got too high and sticks out over the top of the unit square. Let’s play the cobweb game and see which points stay within the unit square. Any point between 1/3 and 2/3 of the diagonal goes out immediately. Show that the point (1/6, 1/6), which lies on the diagonal above the interval [1/9, 2/9], leaves the square. How many steps are required? Likewise, show that the point (5/6, 5/6), which lies on the diagonal above the interval [7/9, 8/9], also leaves the square.