Sketch the graph of a function f that has all of the properties listed. The graph need not be given by an algebraic formula. (a) Continuous and differentiable for all real numbers (b) Increasing on (- o, -3) and (1,3) (c) Decreasing on (-3,1) and (3.00) (d) Concave downward on (-∞, -1) and (2,00) (e) Concave upward on (-1,2) (f) f'(-3) = f'(3) = 0 (g) Inflection points at (-1,4) and (2,5) Choose the correct graph below. O A. G O B. Q Q CIB O C. Q Q O D.
Sketch the graph of a function f that has all of the properties listed. The graph need not be given by an algebraic formula. (a) Continuous and differentiable for all real numbers (b) Increasing on (- o, -3) and (1,3) (c) Decreasing on (-3,1) and (3.00) (d) Concave downward on (-∞, -1) and (2,00) (e) Concave upward on (-1,2) (f) f'(-3) = f'(3) = 0 (g) Inflection points at (-1,4) and (2,5) Choose the correct graph below. O A. G O B. Q Q CIB O C. Q Q O D.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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- **B.**
- **C.**
- **D.**
#### Detailed Explanation of Graph Properties:
- **Continuity and Differentiability:**
The function must be smooth without any breaks, jumps, or sharp corners. Its derivative should exist everywhere.
- **Monotonic Intervals:**
- **Increasing Intervals:**
The function should rise from left to right on the intervals \(( -\infty, -3 )\) and \((1, 3)\).
- **Decreasing Intervals:**
The function should fall from left to right on the intervals \(( -3, 1 )\) and \((3, \infty)\).
- **Concavity:**
- **Concave Downward:**
The function should curve downward like a frown on the intervals \(( -\infty, -1 )\) and \((1, \infty)\).
- **Concave Upward:**
The function should curve upwards like a smile on the interval \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b6dc6c4-2828-4529-a1c7-3495f006d86b%2Fa4c50fca-7551-4bed-b231-8f462ced3f53%2Ft9hmid_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Graphing a Function with Specific Properties
#### Instructions:
Sketch the graph of a function \( f \) that has all of the properties listed below. The graph need not be given by an algebraic formula:
#### Properties:
- **(a)** Continuous and differentiable for all real numbers.
- **(b)** Increasing on \(( -\infty, -3 )\) and \((1, 3)\).
- **(c)** Decreasing on \(( -3, 1 )\) and \((3, \infty)\).
- **(d)** Concave downward on \(( -\infty, -1 )\) and \((1, \infty)\).
- **(e)** Concave upward on \(( -1, 2 )\).
- **(f)** \(f'(-3) = f'(3) = 0\).
- **(g)** Inflection points at \((-1, 4)\) and \((2, 5)\).
#### Task:
Choose the correct graph below:
- **A.**
- **B.**
- **C.**
- **D.**
#### Detailed Explanation of Graph Properties:
- **Continuity and Differentiability:**
The function must be smooth without any breaks, jumps, or sharp corners. Its derivative should exist everywhere.
- **Monotonic Intervals:**
- **Increasing Intervals:**
The function should rise from left to right on the intervals \(( -\infty, -3 )\) and \((1, 3)\).
- **Decreasing Intervals:**
The function should fall from left to right on the intervals \(( -3, 1 )\) and \((3, \infty)\).
- **Concavity:**
- **Concave Downward:**
The function should curve downward like a frown on the intervals \(( -\infty, -1 )\) and \((1, \infty)\).
- **Concave Upward:**
The function should curve upwards like a smile on the interval \
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