Relative Extrema E63E58

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:** A relative maximum is a point where the function changes from increasing to decreasing, and the function value is higher than nearby points. A relative minimum is a point where the function changes from decreasing to increasing, and the function value is lower than nearby points. 3. **Given Information:** - Relative maximum at $x = -2$ with value $0$. - Relative minimum at $x = 0$ with value $-3$. 4. **Verification:** From the graph description: - At $x = -2$, the function reaches a peak (local maximum) at $y = 0$. - At $x = 0$, the function reaches a valley (local minimum) at $y = -3$. 5. **Conclusion:** The relative extrema are: - Relative maximum: $(x, y) = (-2, 0)$ - Relative minimum: $(x, y) = (0, -3)$ These points represent the locations and values of all relative extrema for the function based on the graph provided.