1. The problem states that the curve $y = f(x)$ has a maximum point at $(-3, -6)$. We need to find the maximum point of the transformed curve $y = \frac{1}{2} f(x + 1) + 1$. 2. The transformation involves two operations on $f(x)$: - Horizontal shift: $f(x + 1)$ shifts the graph of $f(x)$ to the left by 1 unit. - Vertical scaling and shift: $\frac{1}{2} f(x + 1)$ compresses the graph vertically by a factor of $\frac{1}{2}$, and adding 1 shifts it up by 1 unit. 3. To find the new maximum point, first find the $x$-coordinate where the maximum occurs in the transformed function. Since the original maximum is at $x = -3$, for $f(x + 1)$ the maximum occurs when $x + 1 = -3$, so: $$x + 1 = -3 \implies x = -4$$ 4. The $y$-coordinate of the maximum point of the transformed function is: $$y = \frac{1}{2} f(-3) + 1 = \frac{1}{2} \times (-6) + 1 = -3 + 1 = -2$$ 5. Therefore, the maximum point of the curve $y = \frac{1}{2} f(x + 1) + 1$ is at: $$\boxed{(-4, -2)}$$