CC MATHEMATICS   CHAOS AND CALCULUSSYLLABUS

Chapter 8 Homework - chaos questions

 

Pair up with a classmate, and hand in a joint solution to the following problem.

 

1.    Consider the function .   What are the roots of this function? 

 

2.    Obtain the Newton function for f(x).  Perform 4 iterations of the Newton function by hand or calculator, starting with the guess of 1.  To what root is this iterative process converging?

 

3.       Now draw a careful plot of this function, including all roots, high points and low points.  (It might be helpful to use a little calculus.) 

 

4.      Use the plot you have drawn to graphically analyze the basins of convergence for the Newton function.  That is, analyze how changing the starting point affects which root Newton’s method converges to.