Prove that the tangent to the graph of the function \(f (x)\), constructed at coordinates \((x_0, f (x_0))\) intersects the \(Ox\) axis at the coordinate: \(x_0 -\frac{f(x_0)}{f'(x_0)}\).
The Newton method (see Problem 61328) does not always allow us to approach the root of the equation \(f(x) = 0\). Find the initial condition \(x_0\) for the polynomial \(f(x) = x (x - 1)(x + 1)\) such that \(f(x_0) \neq x_0\) and \(x_2 = x_0\).