1. The problem asks for the x-coordinate where the curve $y = x^2 - 6x + 7$ has a local minimum. 2. Since this is a quadratic function with leading coefficient $1 > 0$, it opens upwards and thus has a local minimum at its vertex. 3. The x-coordinate of the vertex of a parabola $y = ax^2 + bx + c$ is given by the formula $$x = -\frac{b}{2a}$$ 4. Here, $a = 1$, $b = -6$, so $$x = -\frac{-6}{2\times 1} = \frac{6}{2} = 3$$ 5. Therefore, the local minimum value occurs at $x = 3$. Final answer: (b) 3