-4 nswer Formats Type your answers in interval notation. Use -INF and INF to denote ∞ and co. Enter NONE if it is not positive / negative. If there is more than one interval, type your answer as a comma separated list. For example: (a₁, b₁), (a₂, b₂). art 1: The First Derivative d the open interval(s) on which f'(x) is positive/negative. Type your answers using interval notation. ■. f'(z) is positive: f'(x) is negative: art 2: The Second Derivative d the open interval(s) on which f" (z) is positive/negative. Type your answers using interval notation. ■.f"(z) is positive: f"(z) is negative: te: You can click on the graph to enlarge the image. -3 -2 -1 4 3 2 .1 -2 -3 1 2
-4 nswer Formats Type your answers in interval notation. Use -INF and INF to denote ∞ and co. Enter NONE if it is not positive / negative. If there is more than one interval, type your answer as a comma separated list. For example: (a₁, b₁), (a₂, b₂). art 1: The First Derivative d the open interval(s) on which f'(x) is positive/negative. Type your answers using interval notation. ■. f'(z) is positive: f'(x) is negative: art 2: The Second Derivative d the open interval(s) on which f" (z) is positive/negative. Type your answers using interval notation. ■.f"(z) is positive: f"(z) is negative: te: You can click on the graph to enlarge the image. -3 -2 -1 4 3 2 .1 -2 -3 1 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Graph Description:**
The graph depicts a mathematical function \( f(x) \) with the x-axis ranging approximately from -4 to 2 and the y-axis from -3 to 4. The curve first decreases until about \( x = -3 \), at which point it begins to increase until around \( x = -1 \). It then decreases slightly until around \( x = 1 \) and then increases sharply beyond this point.
---
**Answer Formats:**
- Type your answers in interval notation.
- Use -INF and INF to denote \(-\infty\) and \(\infty\).
- Enter NONE if it is not positive/negative.
- If there is more than one interval, type your answer as a comma-separated list. For example: \((a_1, b_1), (a_2, b_2)\).
---
**Part 1: The First Derivative**
Find the open interval(s) on which \( f'(x) \) is positive/negative. Type your answers using interval notation.
1. \( f'(x) \) is positive: [Input Box]
2. \( f'(x) \) is negative: [Input Box]
---
**Part 2: The Second Derivative**
Find the open interval(s) on which \( f''(x) \) is positive/negative. Type your answers using interval notation.
1. \( f''(x) \) is positive: [Input Box]
2. \( f''(x) \) is negative: [Input Box]
---
**Note:** You can click on the graph to enlarge the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d728491-ca3a-470b-9076-be2816d1a071%2F2153756b-de73-411b-bdf2-854342356066%2F0c15oiu_processed.png&w=3840&q=75)
Transcribed Image Text:**Graph Description:**
The graph depicts a mathematical function \( f(x) \) with the x-axis ranging approximately from -4 to 2 and the y-axis from -3 to 4. The curve first decreases until about \( x = -3 \), at which point it begins to increase until around \( x = -1 \). It then decreases slightly until around \( x = 1 \) and then increases sharply beyond this point.
---
**Answer Formats:**
- Type your answers in interval notation.
- Use -INF and INF to denote \(-\infty\) and \(\infty\).
- Enter NONE if it is not positive/negative.
- If there is more than one interval, type your answer as a comma-separated list. For example: \((a_1, b_1), (a_2, b_2)\).
---
**Part 1: The First Derivative**
Find the open interval(s) on which \( f'(x) \) is positive/negative. Type your answers using interval notation.
1. \( f'(x) \) is positive: [Input Box]
2. \( f'(x) \) is negative: [Input Box]
---
**Part 2: The Second Derivative**
Find the open interval(s) on which \( f''(x) \) is positive/negative. Type your answers using interval notation.
1. \( f''(x) \) is positive: [Input Box]
2. \( f''(x) \) is negative: [Input Box]
---
**Note:** You can click on the graph to enlarge the image.
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