https://file.aiquickdraw.com/mathbot/file/17291869181519qtxes7e.jpg

From the graph provided, we need to identify the intervals where the function is increasing and decreasing.

### Increasing Intervals:
The function is increasing where the slope of the curve is positive (where the curve moves upward). Based on the graph:
- The function is increasing between \( x = -4 \) and \( x = -1 \).
- The function also increases after \( x = 3 \), so the second interval is \( (3, 5] \).

### Decreasing Intervals:
The function is decreasing where the slope of the curve is negative (where the curve moves downward). Based on the graph:
- The function is decreasing between \( x = -1 \) and \( x = 3 \).

### Final Answer:
- **Increasing on the interval(s)**: \( (-4, -1) \cup (3, 5] \)
- **Decreasing on the interval(s)**: \( (-1, 3) \)

Would you like further details on how these intervals were determined?

Here are five follow-up questions that can deepen your understanding:

1. What are critical points, and how do they relate to increasing and decreasing intervals?
2. How can the first derivative of a function help in identifying these intervals?
3. Can a function be increasing or decreasing at a single point, like at a maximum or minimum?
4. How do local maxima and minima relate to the intervals where a function increases or decreases?
5. What is the difference between increasing on an open interval and a closed interval?

**Tip:** Remember, a function's behavior changes at points where the derivative is zero or undefined, typically corresponding to peaks, valleys, or points of inflection.

The function graphed above is: Increasing on the interval(s) __ and Decreasing on the interval(s) __.

Learn how to find the increasing and decreasing intervals of a function based on its graph. This calculus problem covers key concepts such as the first derivative test and graph behavior, 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