Let \( f \) be a twice continuously differentiable function on \( [a, b] \) such that \( f'(x)<0 \) and \( f''(x)<0 \) for all \( x \in (a, b) \). Let \( f(\zeta) = 0 \) for some \( \zeta \in (a, b) \). The Newton-Raphson method to compute \( \zeta \) is given by
\[ x_{k+1} = x_k - \frac{f(x_k)}{f'(x_k)}, \quad k = 0, 1, 2, ...... \]
for an initial guess \( x_0 \).
If \( x_k \in (\zeta, b) \) for some \( k \geq 0 \), then which of the following statements is/are correct?