The figure below shows the graph of f', the derivative of f, on the interval [-5, 4]. The function f is differentiable on the interval and f(-4) = 0. (a) Find f'(-2) and f"(-2). f'(-2) = f"(-2) = -5-4-3-2 X = (b) At which x-values does f have a relative extrema on the interval (-5, 0)? (Enter your answers as a comma-separated list.) 12 (c) Find all intervals on which the graph of f is concave downward. (Enter your answer using interval notation.) X = (d) Find the x-coordinate of each of the points of inflection of the graph of f. (Enter your answers as a comma-separated list.)
The figure below shows the graph of f', the derivative of f, on the interval [-5, 4]. The function f is differentiable on the interval and f(-4) = 0. (a) Find f'(-2) and f"(-2). f'(-2) = f"(-2) = -5-4-3-2 X = (b) At which x-values does f have a relative extrema on the interval (-5, 0)? (Enter your answers as a comma-separated list.) 12 (c) Find all intervals on which the graph of f is concave downward. (Enter your answer using interval notation.) X = (d) Find the x-coordinate of each of the points of inflection of the graph of f. (Enter your answers as a comma-separated list.)
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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![**Graph of the Derivative \( f' \) and Analysis**
The figure above illustrates the graph of \( f' \), the derivative of the function \( f \), on the interval \([-5, 4]\). It is given that the function \( f \) is differentiable on this interval and that \( f(-4) = 0 \).
**Graph Description:**
- The x-axis ranges from -5 to 4.
- The y-axis ranges from -2 to 4.
- Key points on the graph include:
- \( f'(-2) = 0 \)
- \( f'(1) = 0 \)
**Questions:**
(a) **Find \( f'(-2) \) and \( f''(-2) \).**
- \( f'(-2) = \) [Enter answer]
- \( f''(-2) = \) [Enter answer]
(b) **At which x-values does \( f \) have a relative extrema on the interval \((-5, 0)\)?** (Enter your answers as a comma-separated list.)
- \( x = \) [Enter answer]
(c) **Find all intervals on which the graph of \( f \) is concave downward.** (Enter your answer using interval notation.)
- [Enter answer]
(d) **Find the x-coordinate of each of the points of inflection of the graph of \( f \).** (Enter your answers as a comma-separated list.)
- \( x = \) [Enter answer]
**Graph Analysis:**
- There is a change in direction at key points where the graph intersects the x-axis.
- Use these points to determine concavity and points of inflection.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F466923f0-6f55-4935-bc1a-e5c184127f99%2Fa5f41e14-d22a-492a-97fa-a851169a8fe1%2F0qtmrgl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graph of the Derivative \( f' \) and Analysis**
The figure above illustrates the graph of \( f' \), the derivative of the function \( f \), on the interval \([-5, 4]\). It is given that the function \( f \) is differentiable on this interval and that \( f(-4) = 0 \).
**Graph Description:**
- The x-axis ranges from -5 to 4.
- The y-axis ranges from -2 to 4.
- Key points on the graph include:
- \( f'(-2) = 0 \)
- \( f'(1) = 0 \)
**Questions:**
(a) **Find \( f'(-2) \) and \( f''(-2) \).**
- \( f'(-2) = \) [Enter answer]
- \( f''(-2) = \) [Enter answer]
(b) **At which x-values does \( f \) have a relative extrema on the interval \((-5, 0)\)?** (Enter your answers as a comma-separated list.)
- \( x = \) [Enter answer]
(c) **Find all intervals on which the graph of \( f \) is concave downward.** (Enter your answer using interval notation.)
- [Enter answer]
(d) **Find the x-coordinate of each of the points of inflection of the graph of \( f \).** (Enter your answers as a comma-separated list.)
- \( x = \) [Enter answer]
**Graph Analysis:**
- There is a change in direction at key points where the graph intersects the x-axis.
- Use these points to determine concavity and points of inflection.
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Step 1: Question Description
VIEWStep 2: (a) Finding f'(-2), and f''(-2)
VIEWStep 3: (b) Finding x-values for which f has a relative extrema on (-5, 0)
VIEWStep 4: (c) To Find all intervals on which the graph of f is concave downward
VIEWStep 5: (d) To find the x-coordinate of each of the points of inflection
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