Write a function with the following header: function [n iterations, root] = my r

Question

Write a function with the following header: function [n iterations, root] = my root bisection(f, a, b, tolerance) where: _ f is a function handle that represents a continuous real-valued function f de_ned on R. f takes a single input argument that is a scalar of class double (other than NaN, Inf, and -inf) and outputs a single output argument that is a scalar of class double (other than NaN, Inf, and -Inf). _ a and b are scalars of class double such that (b > a) and (f(a)*f(b) > [n, root] = my_root_bisection(my_function, 2, 3, 1e-3) n = 12 root = 2.2361 >> f = @(var) cos(var/2); >> [n, root] = my_root_bisection(f, 3, 4, 1e-5) n = 10 root = 3.1416 >> f = @(x) cos(x)-x; >> [n, root] = my_root_bisection(f, -10, 10, 1e-4) n = 15 root = 0.7391

Explanation / Answer

function result = fun(x)
    result = x*x + 3*x + 2;
end

function [n, root] = my_root_bisection(fn, a, b, tolerance)
   n = 0;
   if fn(a) < fn(b)
    temp = a;
    a = b;
    b = temp;
   end
   root = (a+b)/2;
   while abs(fn(root)) > tolerance
    if fn(root) > 0
        a = root;
    else
        b = root;
    end
    root = (a+b)/2;
    n = n + 1;
   end
end

[n, root] = my_root_bisection(@fun,-5,-1.5,0.00003);
n
root

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