1. **Problem Statement:** Find the local maxima, local minima, absolute maximum, and absolute minimum of the function $f$ on the interval $[0,8]$ based on the given graph. 2. **Local Maximum:** A local maximum occurs where the function changes from increasing to decreasing. 3. **Local Minimum:** A local minimum occurs where the function changes from decreasing to increasing. 4. **Absolute Maximum and Minimum:** The absolute maximum is the highest value of $f$ on $[0,8]$, and the absolute minimum is the lowest value of $f$ on $[0,8]$. 5. **Given Answers from the Graph:** - Local maximum at $x=3$ - Local minima at $x=2$ and $x=5$ - Absolute maximum value is $5$ - Absolute minimum value is $1$ 6. **Summary:** - Local maxima: $x=3$ - Local minima: $x=2, 5$ - Absolute maximum: $5$ - Absolute minimum: $1$