kill(all)$

     Van / facebook.com/LearningCalculus

f(x):=x^3+1;

g(x):=2*(2*x-1)^(1/3);

h(x):=f(x)-g(x)$

newton(t):=subst(t,x,x-h(x)/diff(f(x),x));

newton(newton(1));

f(1); g(1);

makelist([x,h(x)],x,0.6180339887498947,0.6180339887498949,.0000000000000001)$

x1:0.6180339887498948$

h(x1);

f(x1);g(x1);

float(newton(newton(newton(x1))));