Use a graphing utility to graph the function on the closed interval [a, b]. f(x) = |x| - 1, [-4, 4] -4 -2 -2 y 4 -4 -2 2 -4 -2 2. Determine whether Rolle's Theorem can be applied to f on the interval. (Select all that apply.) O Yes, Rolle's Theorem can be applied. O No, because fis not continuous on the closed interval [a, b]. O No, because f is not differentiable in the open interval (a, b). O No, because f(a) * f(b). If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = 0. (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.) %3D
Use a graphing utility to graph the function on the closed interval [a, b]. f(x) = |x| - 1, [-4, 4] -4 -2 -2 y 4 -4 -2 2 -4 -2 2. Determine whether Rolle's Theorem can be applied to f on the interval. (Select all that apply.) O Yes, Rolle's Theorem can be applied. O No, because fis not continuous on the closed interval [a, b]. O No, because f is not differentiable in the open interval (a, b). O No, because f(a) * f(b). If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = 0. (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.) %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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![### Educational Exercise on Rolle's Theorem
#### Problem Statement
Use a graphing utility to graph the function on the closed interval \([a, b]\).
\[ f(x) = |x| - 1,\quad [-4, 4] \]
Graphs of the function \( f(x) \) on the interval \([-4, 4]\):
1.  - Depicts the function \( f(x) \) from \([-4, 4]\).
2.  - Another variation of \( f(x) \) from \([-4, 4]\).
3.  - Additional portrayal of \( f(x) \) on \([-4, 4]\).
4. 
The above graphs illustrate the function \( f(x) = |x| - 1 \) on the interval \([-4, 4]\). Each graph is essentially the same, presenting the V-shaped nature of the absolute value function \( |x| \), which is vertically shifted down by 1 unit.
#### Determine Applicability of Rolle's Theorem
Determine whether Rolle's Theorem can be applied to \( f \) on the interval. (Select all that apply.)
- [ ] Yes, Rolle's Theorem can be applied.
- [ ] No, because \( f \) is not continuous on the closed interval \([a, b]\).
- [ ] No, because \( f \) is not differentiable in the open interval \((a, b)\).
- [ ] No, because \( f(a) \ne f(b) \).
#### Calculation of Values of \( c \)
If Rolle's Theorem can be applied, find all values of \( c \) in the open interval \((a, b)\) such that \( f'(c) = 0 \). (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)
\[ c = \_\_\_\_ \]
#### Explanation of Graphs
Each graph shows the function \( f(x) = |x| - 1 \) with a V-shape characteristic of absolute value functions. The function decreases linearly from \((4, 3)\) to \((0, -1)\) and then](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52a0c9f6-ada1-431f-830a-3fbdcbca3339%2Fa96313f0-4411-4676-a27f-e38d5e78291f%2Fs4u5oj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Exercise on Rolle's Theorem
#### Problem Statement
Use a graphing utility to graph the function on the closed interval \([a, b]\).
\[ f(x) = |x| - 1,\quad [-4, 4] \]
Graphs of the function \( f(x) \) on the interval \([-4, 4]\):
1.  - Depicts the function \( f(x) \) from \([-4, 4]\).
2.  - Another variation of \( f(x) \) from \([-4, 4]\).
3.  - Additional portrayal of \( f(x) \) on \([-4, 4]\).
4. 
The above graphs illustrate the function \( f(x) = |x| - 1 \) on the interval \([-4, 4]\). Each graph is essentially the same, presenting the V-shaped nature of the absolute value function \( |x| \), which is vertically shifted down by 1 unit.
#### Determine Applicability of Rolle's Theorem
Determine whether Rolle's Theorem can be applied to \( f \) on the interval. (Select all that apply.)
- [ ] Yes, Rolle's Theorem can be applied.
- [ ] No, because \( f \) is not continuous on the closed interval \([a, b]\).
- [ ] No, because \( f \) is not differentiable in the open interval \((a, b)\).
- [ ] No, because \( f(a) \ne f(b) \).
#### Calculation of Values of \( c \)
If Rolle's Theorem can be applied, find all values of \( c \) in the open interval \((a, b)\) such that \( f'(c) = 0 \). (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)
\[ c = \_\_\_\_ \]
#### Explanation of Graphs
Each graph shows the function \( f(x) = |x| - 1 \) with a V-shape characteristic of absolute value functions. The function decreases linearly from \((4, 3)\) to \((0, -1)\) and then
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