Use the given graph of the function f to answer the following questions. Answer 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). -4 Part 1: The First Derivative Find the open interval(s) on which f'(z) is positive/negative. Type your answers using interval notation. 1. f'(z) is positive: 2. f'(z) is negative: Part 2: The Second Derivative Find the open interval(s) on which f"(z) is positive/negative. Type your answers using interval notation. 1. f"(z) is positive: 2. f"(z) is negative: Note: You can click on the graph enlarge the image. f(x)
Use the given graph of the function f to answer the following questions. Answer 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). -4 Part 1: The First Derivative Find the open interval(s) on which f'(z) is positive/negative. Type your answers using interval notation. 1. f'(z) is positive: 2. f'(z) is negative: Part 2: The Second Derivative Find the open interval(s) on which f"(z) is positive/negative. Type your answers using interval notation. 1. f"(z) is positive: 2. f"(z) is negative: Note: You can click on the graph enlarge the image. f(x)
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 of the function \( f(x) \) shows a curve with the following features:
- The curve has local minima and maxima within the interval.
- It appears to be a polynomial function with turning points.
### 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 field]
2. \( f'(x) \) is negative:
- [Input field]
### 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 field]
2. \( f''(x) \) is negative:
- [Input field]
**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%2F5bbec5fc-c7ae-435a-8ee1-957b379c17fd%2F7cvkfqu_processed.png&w=3840&q=75)
Transcribed Image Text:**Graph Analysis and Questions**
Use the given graph of the function \( f \) to answer the following questions.
### Graph Description:
The graph of the function \( f(x) \) shows a curve with the following features:
- The curve has local minima and maxima within the interval.
- It appears to be a polynomial function with turning points.
### 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 field]
2. \( f'(x) \) is negative:
- [Input field]
### 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 field]
2. \( f''(x) \) is negative:
- [Input field]
**Note**: You can click on the graph to enlarge the image.
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