Write a MATLAB function, called bisection_method that inputs a function f, two numbers a, b, an error tolerance, tol, and a maximum number of iterations, N, and finds a root c of f in the interval [a, b] using the bisection method. Your function should compute a bound on the error, and stop when the error is less than the tolerance, or if the number of iterations exceeds N - whichever happens first. • Hint #1: The function should start with the line function [c, n,err] = bisection_method(f, a,b, tol, N)
• Hint #2: The function should contain a ‘while’ loop, looking something like: while err > tol && n < N
c) Use the code that you developed in Problem 2 to solve f(x)-(2t3 + 3x-1) cos(x)-x 0 in [-1, 1, for an accuracy of 10
i. What is the number, n of iterations used?
ii. What is the error bound?
iii. What is the expected rate of convergence?
iv. Plot on the same graph the function f and the axis y 0.
v. Using the built-in function solve from Matlab, compute the exact root and compare to your solution