1. Let's start by understanding the problem: You want to know why it is important to identify when a graph is at rest. 2. In mathematics and physics, a graph is "at rest" when its rate of change (or slope) is zero. This means the function's derivative equals zero: $$f'(x) = 0$$. 3. This condition is crucial because it helps us find critical points such as maxima, minima, or points of inflection on the graph. 4. Knowing when the graph is at rest allows us to understand the behavior of the function, such as where it stops increasing or decreasing. 5. For example, in physics, when a velocity-time graph is at rest (velocity zero), it indicates the object is momentarily stopped. 6. In optimization problems, finding where the graph is at rest helps locate optimal values. 7. Therefore, identifying when the graph is at rest is essential for analyzing and interpreting the function's behavior effectively.