https://file.aiquickdraw.com/mathbot/file/1725390518633b7idm2hx.jpg

To analyze the graph of the function and determine where it is increasing or decreasing, follow these steps:

1. **Increasing Intervals**: A function is increasing on an interval where the graph is moving upwards as you move from left to right.

2. **Decreasing Intervals**: A function is decreasing on an interval where the graph is moving downwards as you move from left to right.

**Steps to solve the problem:**

- **Identify Critical Points**: Look at where the function changes direction, i.e., where it has peaks (local maxima) or troughs (local minima). These points will help you determine the intervals.

**Observations from the Graph:**

1. The graph decreases from \( x = -\infty \) to about \( x = -1 \).
2. It increases from \( x = -1 \) to \( x = 1 \).
3. It decreases again from \( x = 1 \) to about \( x = 3 \).
4. Finally, it increases from \( x = 3 \) onwards.

**Therefore:**

- **Increasing Intervals:** The function is increasing on the intervals \((-1, 1)\) and \((3, \infty)\).
- **Decreasing Intervals:** The function is decreasing on the intervals \((-\infty, -1)\) and \((1, 3)\).

Would you like further details or have any questions?

Here are 5 related questions:
1. What are local maxima and minima, and how do they relate to increasing and decreasing intervals?
2. How would you determine the intervals of concavity from a graph?
3. What is the importance of the first derivative in identifying increasing and decreasing intervals?
4. How can you determine whether a function is increasing or decreasing using algebraic methods?
5. How do points of inflection affect the intervals of increase and decrease in a function?

**Tip:** When analyzing graphs, always note the behavior of the function around critical points to determine the nature of intervals.

The function graphed above is: Increasing on the interval(s) ___, Decreasing on the interval(s) ___.

Learn how to determine the intervals where a function is increasing or decreasing by analyzing its graph. This problem covers key calculus concepts such as graph analysis and the first derivative test. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation