Subjects calculus

Function Interval Behavior D2F915

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1. **Stating the problem:** We want to analyze the behavior of the function on the interval $6 < x < 7$ based on the graph description. 2. **Understanding the graph:** The function has a peak around $x=6$, meaning it reaches a local maximum there. 3. **Behavior near $x=6$:** Since the function is increasing before $x=6$ and has a peak at $x=6$, it must start decreasing after $x=6$. 4. **Sign of the function on $6 < x < 7$:** The function crosses the x-axis near $x=7$, so between $6$ and $7$, the function is still above the x-axis (positive). 5. **Conclusion:** On the interval $6 < x < 7$, the function is positive and decreasing. **Final answer:** The function is positive and decreasing on the interval $6 < x < 7$.