Roots with Bisection and Newton Raphson methods

Hi,

How can I write a single script which tries to find the roots of the following functions using both the Bisection and Newton Raphson methods? Also I want to generate a plot of the functions showing the location of the initial guess(es) and the approximated root value..

Function Interval Tolerance

f(x) = 2sin(x) + 2cos(x) [-1 1] 1x10-3

f(x) = 2-sin(x) – x2 [-1 2] 1x10-4

[madhan ravi]

upload the code that you tried

[Utku Palakci]

myFunction = @(x) 2.*sin(x) + 2.*cos(x);

x_lower =
x_upper = 

while abs(myFunction(x_mid) > 
    if (myFunction(x_mid) * myFunction(x_upper)) < 0
        x_lower = x_mid;
    else
        x_upper = x_mid;
    end
    x_mid = (x_lower + x_upper)/2;
end

fprintf('The root is \g\n', x_mid) %#ok<CTPCT>

% For the first function with Bisection. How do I find the lower and upper limits?

[Cris LaPierre]

This is a very common numerical methods assignment. Have you tried searching the forum yet? Chances are this question has already been answered many times.

[Jan]

This line is incomplete:

while abs(myFunction(x_mid) >

How do I find the lower and upper limits? - You have to guess them. There is no way to find then in advance.