1. The problem asks for the minimum integer $n$ such that $|f(\alpha)| \leq 10^{-6}$, where $\alpha$ is the root at point B and $x_{n+1}$ is the iteration step. 2. Typically, this relates to the convergence of an iterative method for finding roots, where $x_{n+1}$ is the next approximation and $f(\alpha) = 0$ since $\alpha$ is a root. 3. The condition $|f(\alpha)| \leq 10^{-6}$ means the function value at the root approximation is within $10^{-6}$ of zero, indicating high accuracy. 4. Since $\alpha$ is the root at point B, and the question asks for the minimum $n$ in $x_{n+1}$ such that the function value is sufficiently small, the answer corresponds to the iteration count needed to reach this precision. 5. From the given options (A. 3, B. 4, C. 5, D. 6), the minimum $n$ satisfying $|f(\alpha)| \leq 10^{-6}$ is $4$. 6. Therefore, the answer is B. 4.