function w = Newton

%MATLAB routine for visualizing the workings of Newton's method
%Created by Winfried Just, department of Mathematics, Ohio University
%Last modified: January 28, 2003

syms x 

disp(' ')
input('Enter the formula for your function. \n');

f = ans
g = diff(f);

disp(' ')
input('Enter the initial value of x. \n');

x0 = ans

disp(' ')
input('Enter the left endpoint of your interval for $x$. \n');

a = ans

disp(' ')
input('Enter the right endpoint of your interval for $x$. \n');

b = ans

disp(' ')
input('Enter the lower limit of the y-axis. \n');

c = ans

disp(' ')
input('Enter the upper limit of the y-axis. \n');

d = ans



y = subs(f, x0);



hold off;
ezplot('0', [a,b])
hold on;
ezplot(f, [a,b])
axis([a b c d])

while 0 < 1
    disp(' ')
    disp('Hit ENTER to continue of Ctrl^C to quit')
    pause
  
    m = subs(g, x0); %the slope of f at x0
    y = subs(f, x0); %the value f(x0)
    h = m*(x-x0) + y;
    
    ezplot(h, [a,b])
    
    x0 = x0 - y/m;
    
    axis([a b c d])
    disp('The current approximation is:')
    disp(x0)
      
end