kill(all)$

fpprintprec:6$

van=facebook.com/LearningCalculus$

f(x):=x^x-100$

newton(t):=float(subst(t,x,x-f(x)/diff(f(x),x)))$

q[i]:=newton(q[i-1])$

q[1]:newton(3);

n:8$

Y:create_list(q[i],i,2,n);

Y:cons(q[1],Y);

X:create_list(i, i, 1,n);

XY:create_list([X[i],Y[i]],i,1,n);

plot2d([[discrete, XY],[discrete, XY]],[x,1,n],[y, 3,5], 
        [style, lines, points], [color, red, black],
        [point_type, bullet],
        [legend, "x vs Newton iteration"],
        [xlabel, "iteration"],
        [ylabel, "x"],[gnuplot_preamble,"set size ratio 1;"])$