Assignment 9/6:  Due Tuesday 9/10 at 3 PM

Turn in individual solutions. You may work together in solving the problems, or get help from others, but the final write-up should be your own. Do not turn in anything you cannot explain completely.

   Calculus (ON ALL OF THESE PROBLEMS, DO THE DERIVATIVES BY THE DEFINITION (DELTA X METHOD)
            P84-85 #16, 18acg, 19c (on this one also find the equation of the tangent line and graph it and the original function in the same graph), 24

   Calculus Under Control Problem 5.2, page 394.  

1. Consider the logistic map defined by s=3.1. That is, you are considering the dynamical system determined by the parabola f(x)=3.1(x(1-x)) .
   1. Determine all fixed points for this dynamical system.  Tell whether each is stable.  
   2. According to the  text  (p169),  there is an attractive 2-cycle for this dynamical system. Set up the equation f(f(x))=x, and find the solutions to this equation, using a calculator or computer (describe how you do this). Do you get the values reported in the text? 
      How can you tell that this is stable?