1. The problem asks if the function defined on the interval $(1,2]$ has a maximum value. 2. To determine this, we need to know the function's behavior on the interval $(1,2]$. 3. Since no function is given, let us analyze the interval properties: it is a right-closed, left-open interval. 4. A maximum on $(1,2]$ must be the largest function value attained at some point $x$ in $(1,2]$. 5. Because the interval is closed at $2$, the function value at $x=2$ is included, so if the function is continuous, it may attain its max at $x=2$. 6. However, no explicit function is provided, so we cannot confirm the max value. 7. If you provide a specific function, I can help verify if a maximum exists and find it.