Remember to indent the bodies of your IF-THEN and looping structures.

For the problems below that require you to implement the bisection
method you should use a value of 10^{-10} for each of the tolerances.
Note, in order to assign a value of 10^{-10} in MATLAB, you should do

tol = 1.0e-10If you enter

tol = 10.0e-10then your tolerance will be 10

- 1)
- (3 pts) Write a function to implement Newton's Method.
Use the approach from Problem 2 of HW 18. You will need to
create functions to evaluate both
*f*(*x*) and its derivative and send both of these in as inputs. - 2)
- (8 pts) Repeat Problem 3 of HW 18. Use Newton's Method
to find the roots of the three problems below using the indicated
initial guess:
- a)
- b)
- c)

For each case, you should print out the value of the root, the value of the function at the root, the number of iterations, the status variable and create plots of the convergence histories. How do the iteration counts for Newton's Method compare to the bisection method? For Part c), does Newton's method converge to the same root as the bisection method?

- 3)
- (3 pts) Use Newton's Method to solve

What happens in this case? Verify your conjecture by computing the first few steps of Newton's Method by hand. Can you fix this problem by changing the initial guess?