%% Example 3. Newton’s method
clear all, close all, clc
format longG
x=-1:0.01:6;
f=@(x)1/2*(x-1) + 1/2*(y+2);
f=@(x)sin(x+2) - y;
plot(x,f(x),'r','LineWidth',3)
grid

figure
x=0.8:0.01:1.2;
plot(x,f(x),'r','LineWidth',3)

% Example 2 (continuation)
XN=[0.92 1.08 3]; % initial approximations
iter=5; % maximum number of iterations
syms x, fder(x)=diff(f(x),x);
for j=1:3
    xn=XN(j);
    for i=1:iter
        xn=xn-f(xn)/double(fder(xn));
        M(i,1)=xn; M(i,2)=f(xn);
    end
    disp('initial approximation:'),disp(XN(j))
    disp('              x                 f(x)')
    disp(M)
end