1. **Problem Statement:** We have a graph of speed (in miles per hour) as a function of time (in hours). We want to understand what it means when this function is increasing or decreasing. 2. **Understanding the function:** The function $s(t)$ represents speed at time $t$. The graph shows how speed changes over time. 3. **When the function is increasing:** This means that as time $t$ increases, the speed $s(t)$ also increases. Mathematically, the derivative $s'(t) > 0$. 4. **Interpretation:** If $s(t)$ is increasing, the speed is getting faster over time. 5. **When the function is decreasing:** This means that as time $t$ increases, the speed $s(t)$ decreases. Mathematically, $s'(t) < 0$. 6. **Interpretation:** If $s(t)$ is decreasing, the speed is slowing down over time. **Final answer:** - When the graph is increasing, the speed is increasing. - When the graph is decreasing, the speed is decreasing.