I only need help with part C!

G:x-> 2x.

This function has a unique fixed point at x=0. For what starting value(s) p0 does fixes point iteration converge to it? What happens other wise ?

1. Implement fixed point iteration. Your signature should be function p fp(g, po, maxits) where g is a function handle and pO, maxits, and p are numbers. The return value p is the result of applications of g, i.e., maxits P 8(8(po))) Test your code on the following four functions. (a) g: (x +2/x)/2. (This is the Babylonian method' for computing V2-1.414) i. Confirm visually that the fixed-point problem "Solve g(x)iseqivalent to the root-finding problem "Solve f(z) = 0, with f: z- 2-2. That is, make a plot showing that y f(r) intersects y =0 at the same r-values which y() intersects y . Experiment with the parameters pO and maxits. How can you pick po to control which of the two fixed points (z = V2) the method converges to? ili. Try po 1.5 and compare with the bisection method (Worksheet 3) with a 1, b-2, and tol- eps. Plot the error (abs (sqrt (2) -p) of the two methods as a function of iteration number. (You will have to modify your fp and bisection codes to return all of the iterates, not just the last.) Use a semilogy plot (b) g: cos(x). i, Plot y =g(z) and y-x to visually confirm that g has a unique fixed point. i. Plot the error as a function of iteration number, using the converged value as the exact solution. ii. (Challenge; ungraded) Estimate the rate at which the error (as a function of iteration number n) converges (to zero) when po 1. Do this by fitting a curve of the form n Cq" to the error (c) g:z 2. This function has a unique fixed point at r - 0. For what starting value(s) po does fixed point iteration converge to it? What happens otherwise