1. **Problem statement:** Identify the local maxima of the function $f$ on the interval $(0,8)$ given the graph description. 2. **Recall the definition:** A local maximum at $x=c$ means $f(c)$ is greater than values of $f(x)$ near $c$. 3. **From the graph description:** The function has local maxima near $x=3$ and at the boundary $x=8$. 4. **Explanation:** At $x=3$, the function rises before and falls after, indicating a local maximum. 5. **At $x=8$ (boundary):** Since the function is increasing toward $x=8$, and $x=8$ is the endpoint, it is considered a local maximum on the interval. 6. **Final answer:** The function $f$ has local maxima at $x=3$ and $x=8$ on $(0,8)$.