function [x,H]=newton(f,df,x0,tol)
%NEWTON newton method 
%X=NEWTON(F,DF,X0,TOL) gives by the Newton method an approximation
%X of the zero of the function F with derivative DF.
%X0 is an initial guess for the zero.
%The approximation X is such that ABS(F(X))<=TOL.
%
%[X,H]=NEWTON(F,DF,X0,TOL) also gives a two columns matrix H:
%The first column has the successive iterates generated by the method
%and the second column has the values of F on these iterates.

x=x0;
fx=f(x);
H=[x fx];
while norm(fx)>tol
    dfx=df(x);
    x=x-fx/dfx;
    fx=f(x);
    H(end+1,:)=[x fx];
end