Relative Extrema 4588E2

1. **Problem Statement:** Find the locations and values of all relative extrema (relative maxima and minima) for the given function based on its graph. 2. **Understanding Relative Extrema:** Relative extrema are points where the function changes direction from increasing to decreasing (relative maximum) or from decreasing to increasing (relative minimum). 3. **Given Information:** - Relative maximum at $x = -2$ with value $0$. - Relative minimum at $x = 0$ with value $-3$. 4. **Explanation:** - At $x = -2$, the function reaches a peak (highest point locally), so this is a relative maximum. - At $x = 0$, the function reaches a valley (lowest point locally), so this is a relative minimum. 5. **Summary of Relative Extrema:** - Relative maximum: $(x, y) = (-2, 0)$ - Relative minimum: $(x, y) = (0, -3)$ These points match the description of the graph's shape and the locations where the function changes direction.