7) Approximating Roots (Newton's Method)

Consider the function f(x)

> f:=x->x^3-2*x-1;

> plot(f(x),x=-3..3,-5..5);

The newton method formula is given by the recurrence formula

> newton:=x->x-f(x)/D(f)(x);

As is needed near the root guess

> evalf(newton(-.5));

> evalf(newton(%));

> evalf(newton(%));

> evalf(newton(%));

> evalf(newton(%));