Questions: List the interval(s) on which the function is increasing. (-∞,-6],[-2,-1] List the interval(s) on which the function is decreasing. [-6,-5] List the interval(s) on which the function is constant. [-5,-2][-1, ∞)

List the interval(s) on which the function is increasing. (-∞,-6],[-2,-1] List the interval(s) on which the function is decreasing. [-6,-5] List the interval(s) on which the function is constant. [-5,-2][-1, ∞)
Transcript text: List the interval(s) on which the function is increasing. \[ (-\infty,-6],[-2,-1] \] List the interval(s) on which the function is decreasing. \[ [-6,-5] \] List the interval(s) on which the function is constant. \[ [-5,-2][-1, \infty) \]
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Solution

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Solution Steps

To determine the intervals on which a function is increasing, decreasing, or constant, we typically analyze the derivative of the function. However, since the intervals are already provided, we can directly list them. The function is increasing on the given intervals, decreasing on the specified interval, and constant on the remaining intervals.

Step 1: Understanding the Problem

The problem provides intervals for a function and asks us to identify which intervals correspond to the function being increasing, decreasing, or constant. We need to list these intervals in the appropriate categories.

Step 2: Listing Increasing Intervals

The problem states that the function is increasing on the intervals: \[ (-\infty, -6], [-2, -1] \] These intervals are already provided in interval notation, and no further calculation is needed.

Step 3: Listing Decreasing Intervals

The problem states that the function is decreasing on the interval: \[ [-6, -5] \] This interval is also provided in interval notation.

Step 4: Listing Constant Intervals

The problem states that the function is constant on the intervals: \[ [-5, -2], [-1, \infty) \] These intervals are provided in interval notation, and no further calculation is needed.

Final Answer

  • The interval(s) on which the function is increasing: \(\boxed{(-\infty, -6], [-2, -1]}\)
  • The interval(s) on which the function is decreasing: \(\boxed{[-6, -5]}\)
  • The interval(s) on which the function is constant: \(\boxed{[-5, -2], [-1, \infty)}\)
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