Use the graph of f to find the largest open interval on which f is increasing, and the largest open interval on which f is decreasing. (Enter your answers using interval notation.) -2 y 6 4 2 -2 2 4 X (a) Find the largest open interval(s) on which f is increasing. (If two open intervals are equally large enter your answer as a comma-separated list of intervals.) (b) Find the largest open interval(s) on which f is decreasing. (If two open intervals are equally large enter your answer as a comma-separated list of intervals.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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.
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
Step 1

The open interval is represented using: (   ) and the closed interval is represented using:     .

A function is increasing in the interval: a, b, if f(a)<f(b) for a<b. A function is decreasing in the interval: a, b, if f(a)>f(b) for a<b.

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