#1.b


nodes = linspace(-2,4,10);
f=@(x)(x+1)./(3*x.^2+2*x+1);

plot(nodes, f(nodes),'o');
hold on


x=linspace(-2,4,500);


plot(x,f(x));
hold on

lnf=lagrange_classic(nodes,f(nodes),x);

plot(x,lnf)

plot(x,abs(f(x)-lnf),'x')


nodes = [81,100,121];

f_nodes = [9,10,11];

sqrt(118);
lnf = lagrange_classic(nodes,f_nodes, [118]);


nodes = [1980,1990,2000,2010,2020];
f_nodes = [4451,5287,6090,6970,7821];

lnf = lagrange_barycentric(nodes, f_nodes, [2005,2015])

abs([6474,7405] - lnf)