Answer:
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Explanation:
To determine the intervals of increase and decrease for a graph, we need to analyze the slope of the graph at different points.
1. Identify the points where the slope changes from positive to negative or vice versa. These points are known as critical points or turning points.
2. Determine the sign of the slope on each side of the critical points.
- If the slope is positive (+) to the left of a critical point and negative (-) to the right, it indicates a decreasing interval.
- If the slope is negative (-) to the left of a critical point and positive (+) to the right, it indicates an increasing interval.
- If the slope remains positive (+) or negative (-) on both sides of a critical point, it indicates a constant interval.
Let's apply this process to the given graph:
1. Identify the critical points:
- Critical point 1: The point where the graph changes from increasing to decreasing.
- Critical point 2: The point where the graph changes from decreasing to increasing.
2. Determine the sign of the slope on each side of the critical points:
- Before critical point 1, the slope is positive (+).
- After critical point 1 and before critical point 2, the slope is negative (-).
- After critical point 2, the slope is positive (+).
3. Based on the sign of the slope:
- The interval before critical point 1 is an increasing interval.
- The interval between critical point 1 and critical point 2 is a decreasing interval.
- The interval after critical point 2 is an increasing interval.
Therefore, the intervals of increase and decrease for the graph shown are as follows:
- Increasing interval: Before critical point 1 and after critical point 2.
- Decreasing interval: Between critical point 1 and critical point 2.