function p=false_position(f,p0,p1,tol,max_iterations)

% Method of false position: See section 2.3.
% Use variables q0 and q1 to store f(p0) and f(p1).
% This reduces the number of times we need to evaluate f.
q0=f(p0);
q1=f(p1);

for i=1:max_iterations
    % Store the last two iterations in p0 and p1.
    p = p1 - q1 * (p1-p0)/(q1-q0);
    q = f(p);
    if abs(p-p1)<tol
        return
    end
    % Only update (p0,q0) if p1 and p bracket a root.
    if q*q1 < 0
        p0=p1;
        q0=q1;
    end
    p1=p;
    q1=q;
end
error('Exceeded maximum number of iterations');