https://file.aiquickdraw.com/mathbot/file/1727276110914weihaz5p.jpg

To determine where the function is increasing, decreasing, and constant from the given graph, let’s analyze its behavior based on the plotted curve:

### 1. **Intervals where the function is increasing**:
   - The function increases when moving to the right along the curve and the graph rises. 
   - This occurs in the interval from \(x = -6\) to \(x = -4\), and from \(x = 0\) to \(x = 2\).

### 2. **Intervals where the function is decreasing**:
   - The function decreases when moving to the right and the graph falls.
   - This occurs in the interval from \(x = -4\) to \(x = -2\).

### 3. **Intervals where the function is constant**:
   - The function is constant where the graph is a horizontal line (no change in \(y\)-values).
   - This occurs in the interval from \(x = 2\) to \(x = 6\).

### Final Results:
- **Increasing intervals**: \( (-6, -4) \cup (0, 2) \)
- **Decreasing intervals**: \( (-4, -2) \)
- **Constant intervals**: \( (2, 6) \)

Would you like further details or clarification? 

Here are 5 questions related to this topic:
1. How can we determine whether a function is increasing or decreasing from its derivative?
2. What does a constant function imply about the slope of the function in that interval?
3. How can we identify turning points in a graph?
4. Can a function have multiple intervals of constant values?
5. What is the significance of critical points in determining increasing or decreasing behavior?

**Tip**: The first derivative of a function gives critical information about where the function is increasing or decreasing. A positive derivative means increasing, and a negative derivative means decreasing.

Determine the intervals on which the function is increasing, decreasing, and constant based on the given graph.

Learn how to determine where a function is increasing, decreasing, and constant by analyzing its graph. This problem focuses on key calculus concepts such as increasing and decreasing functions, turning points, and constant intervals. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation