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
