= 6.2.2. The graphs shown in Exercise 1 were plotted from the formula fu(2) = px?(1 - 0). (a) Find the derivative fu'(x) and verify that the derivative is 0 when x = 0 and when x = 2/3. (b) Show that fu maps the interval [0, 1] into itself if 0 su 527 (c) Find the fixed points of fu algebraically and show that they are given by x = 0 and, for u > 4, by x = (1 + V1 - 4/)/2 (d) Verify that the derivative of fu at these fixed points is given by - fu'(x) = 3 - 4 VMP 44 F 2 2 (e) Use the results from parts (c) and (d) to sketch a bifurcation diagram for the fixed points of the family u fu. Compare the result with your answer to Exercise 1. - = 6.2.2. The graphs shown in Exercise 1 were plotted from the formula fu(2) = px?(1 - 0). (a) Find the derivative fu'(x) and verify that the derivative is 0 when x = 0 and when x = 2/3. (b) Show that fu maps the interval [0, 1] into itself if 0 su 527 (c) Find the fixed points of fu algebraically and show that they are given by x = 0 and, for u > 4, by x = (1 + V1 - 4/)/2 (d) Verify that the derivative of fu at these fixed points is given by - fu'(x) = 3 - 4 VMP 44 F 2 2 (e) Use the results from parts (c) and (d) to sketch a bifurcation diagram for the fixed points of the family u fu. Compare the result with your answer to Exercise 1