Hi,

I assume that you know Newton's rule.

\(\displaystyle x_{n+1}=x_{n}-\frac{f(x_n)}{f'(x_n)}\)

With your function this formula becomes:

\(\displaystyle x_{n+1}=x_{n}-\frac{x_n^3-x_n^2-1}{3x_n^2-2x_n}\)

Now \(\displaystyle x_1 = 1\). Thus

\(\displaystyle x_{2}=1-\frac{1-1-1}{3-2}= 2\)

\(\displaystyle x_{3}=2-\frac{8-4-1}{12-4}= 1.625\)

...

\(\displaystyle x_{7}\approx 1.465571232\)

EB