1. The problem states that the curve $y=f(x)$ has a maximum point at $(2,3)$. 2. We need to find the maximum point of the curve $y=2f(x-1)$. 3. The transformation $y=2f(x-1)$ involves two changes: - Horizontal shift: $x$ is replaced by $x-1$, which shifts the graph 1 unit to the right. - Vertical stretch: the function is multiplied by 2, which stretches the graph vertically by a factor of 2. 4. Since the original maximum is at $x=2$, after shifting right by 1, the new maximum $x$-coordinate is: $$x_{new} = 2 + 1 = 3$$ 5. The original maximum $y$-value is 3. After vertical stretching by 2, the new $y$-value is: $$y_{new} = 2 \times 3 = 6$$ 6. Therefore, the maximum point of $y=2f(x-1)$ is at: $$(3, 6)$$