//example 3.14
//lagrange's interpolation formula
//page 105
clc;clear;close;
y=[4 12 19];
x=[1 3 4];
y_x=7;
Y_X=0;
poly(0,'y');
for i=1:3
    p=x(i);
    for j=1:3
        if i~=j then
            p=p*((y_x-y(j) )/( y(i)-y(j)))
        end
    end
    Y_X=Y_X+p;
    end
disp(Y_X,'Y_X=');