>> x=1:0.1:6;>> y=5+7.*(x-1)-1.333.*(x-1).*(x-2)+0.442.*(x-1).*(x-2).*(x-4);>> y1=5+7.*(x-1)-1.333.*(x-1).*(x-2);>> y2=12+3.*(x-2)+(7.*(x-2).*(x-4)/8);>> y3=-((x-2).*(x-4).*(x-6)/3)+(3/2).*(x-1).*(x-4).*(x-6)...-(3/2).*(x-1).*(x-2).*(x-6)+(31/40).*(x-1).*(x-2).*(x-4);>> y4=(5/3).*(x-2).*(x-4)-6.*(x-1).*(x-4)+3.*(x-1).*(x-2);>> y5=(3/2).*(x-4).*(x-6)-(9/2).*(x-2).*(x-6)+(31/8).*(x-2).*(x-4);>> plot (x,y,'xg')>> plot (x,y3)>> plot (x,y,'xg')>> hold on>> plot (x,y3,'g')>> hold on>> plot (x,y1,'xr')>> hold on>> plot (x,y4,'r')>> hold on>> plot (x,y2,'xb')>> hold on>> plot (x,y5,'b')>> hold on>> plot (1,5,'.k')>> plot (2,12,'.k')>> plot (4,18,'.k')>> plot (6,31,'.k')>> grid>> text(1,5,'(1,5)')>> text(2,12,'(2,12)')>> text(4,18,'(4,18)')>> text(6,31,'(6,31)')>> title('Lagrange Interpolating Polynomial vs Newtons Divided-Difference Method')>> xlabel('x-axis')>> ylabel('y-axis')