Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![### Graph Analysis in Calculus
**Objective:**
Examine the graph of the function \( f \) to determine:
- The largest open interval where \( f \) is increasing.
- The largest open interval where \( f \) is decreasing.
**Graph Description:**
- **Axes:** The graph is plotted in the Cartesian plane with the x-axis labeled from -4 to 8 and the y-axis from -4 to 6.
- **Function \( f \):** It appears as a continuous blue curve with notable features such as increasing and decreasing behavior and inflection points.
**Graph Features:**
- The function decreases from the far left, passes through a minimum at \( x \approx -1 \), then increases until \( x \approx 2 \).
- It declines sharply from \( x \approx 2 \) to \( x \approx 3 \).
- \( f \) increases again from \( x \approx 3 \) to \( x \approx 5 \).
- The function decreases steeply after \( x \approx 5 \), hitting a minimum, and then starts slightly increasing past \( x \approx 6 \).
**Exercises:**
(a) **Increasing Interval(s):**
Find the largest open interval(s) where the function \( f \) is increasing. If two intervals are equally large, list both separated by a comma.
**Answer Box:** [ ]
(b) **Decreasing Interval(s):**
Find the largest open interval(s) where the function \( f \) is decreasing. If two intervals are equally large, list both separated by a comma.
**Answer Box:** [ ]
**Need Help?**
For additional guidance, click on the "Read It" button for hints and explanations.
---
This exercise aims to enhance your understanding of function behavior over intervals using graphical interpretation.](https://content.bartleby.com/qna-images/question/7f2e4691-a97f-4dde-8d01-e6164df6c02d/b6f858f0-1a60-4878-a186-7323e495fe54/7kfs0y8_processed.jpeg)
Transcribed Image Text:### Graph Analysis in Calculus
**Objective:**
Examine the graph of the function \( f \) to determine:
- The largest open interval where \( f \) is increasing.
- The largest open interval where \( f \) is decreasing.
**Graph Description:**
- **Axes:** The graph is plotted in the Cartesian plane with the x-axis labeled from -4 to 8 and the y-axis from -4 to 6.
- **Function \( f \):** It appears as a continuous blue curve with notable features such as increasing and decreasing behavior and inflection points.
**Graph Features:**
- The function decreases from the far left, passes through a minimum at \( x \approx -1 \), then increases until \( x \approx 2 \).
- It declines sharply from \( x \approx 2 \) to \( x \approx 3 \).
- \( f \) increases again from \( x \approx 3 \) to \( x \approx 5 \).
- The function decreases steeply after \( x \approx 5 \), hitting a minimum, and then starts slightly increasing past \( x \approx 6 \).
**Exercises:**
(a) **Increasing Interval(s):**
Find the largest open interval(s) where the function \( f \) is increasing. If two intervals are equally large, list both separated by a comma.
**Answer Box:** [ ]
(b) **Decreasing Interval(s):**
Find the largest open interval(s) where the function \( f \) is decreasing. If two intervals are equally large, list both separated by a comma.
**Answer Box:** [ ]
**Need Help?**
For additional guidance, click on the "Read It" button for hints and explanations.
---
This exercise aims to enhance your understanding of function behavior over intervals using graphical interpretation.
Expert Solution
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Step 1
The open interval is represented using: and the closed interval is represented using: .
A function is increasing in the interval: , if for . A function is decreasing in the interval: , if for .
Step by stepSolved in 2 steps
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