Let \( f(x) = x^4 + 2x^3 - 11x^2 - 12x + 36 \) for \( x \in \mathbb{R}. \)
The order of convergence of the Newton-Raphson method
\[
x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}, n \geq 0,
\]
with \( x_0 = 2.1 \), for finding the root \( \alpha = 2 \) of the equation \( f(x) = 0 \) is \(\underline{\hspace{1cm}}\) .