clear
format compact
format long

x1 = .01;
x = newton(@f, @dfdx, x1, 20);

number_of_iterations = length(x) 

np = 100;
t1 = linspace(-10*x1, 10*x1, np);
figure(1)
plot(t1, f(t1), '-')
grid on

t2 = logspace(-3, 3, np);
figure(2)
semilogx(t2, f(t2), '-')
grid on
hold on
for i = 1:length(x)
    semilogx(x(i), f(x(i)), 'x')
end

function y = f(x)
% F demonstrate the case of divergence for Newton's method
    alpha = 0.009;
    y = x./(alpha^2 + x.^2);
end

function y = dfdx(x)
% DFDX demonstrate the case of divergence for Newton's method
    alpha = 0.009;
    y = (alpha^2 - x^2)/(alpha^2 + x^2)^2;
end