Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = x³ 3x + 5, [-2, 2] O Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem. O Yes, f is continuous on [-2, 2] and differentiable on (-2, 2) since polynomials are continuous and differentiable on R. O No, f is not continuous on [-2, 2]. O No, f is continuous on [-2, 2] but not differentiable on (-2, 2). O There is not enough information to verify if this function satisfies the Mean Value Theorem.
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = x³ 3x + 5, [-2, 2] O Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem. O Yes, f is continuous on [-2, 2] and differentiable on (-2, 2) since polynomials are continuous and differentiable on R. O No, f is not continuous on [-2, 2]. O No, f is continuous on [-2, 2] but not differentiable on (-2, 2). O There is not enough information to verify if this function satisfies the Mean Value Theorem.
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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![**Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?**
\( f(x) = x^3 - 3x + 5 \), \([-2, 2]\)
1. ○ Yes, it does not matter if \( f \) is continuous or differentiable; every function satisfies the Mean Value Theorem.
2. ○ Yes, \( f \) is continuous on \([-2, 2]\) and differentiable on \((-2, 2)\) since polynomials are continuous and differentiable on \(\mathbb{R}\).
3. ○ No, \( f \) is not continuous on \([-2, 2]\).
4. ○ No, \( f \) is continuous on \([-2, 2]\) but not differentiable on \((-2, 2)\).
5. ○ There is not enough information to verify if this function satisfies the Mean Value Theorem.
**If it satisfies the hypotheses, find all numbers \( c \) that satisfy the conclusion of the Mean Value Theorem.** (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F657031eb-39bc-4c4b-9506-093cbbf26dd7%2F070ba45f-5814-4ca4-a437-32dba9a3baf3%2F1h4mmmq_processed.png&w=3840&q=75)
Transcribed Image Text:**Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?**
\( f(x) = x^3 - 3x + 5 \), \([-2, 2]\)
1. ○ Yes, it does not matter if \( f \) is continuous or differentiable; every function satisfies the Mean Value Theorem.
2. ○ Yes, \( f \) is continuous on \([-2, 2]\) and differentiable on \((-2, 2)\) since polynomials are continuous and differentiable on \(\mathbb{R}\).
3. ○ No, \( f \) is not continuous on \([-2, 2]\).
4. ○ No, \( f \) is continuous on \([-2, 2]\) but not differentiable on \((-2, 2)\).
5. ○ There is not enough information to verify if this function satisfies the Mean Value Theorem.
**If it satisfies the hypotheses, find all numbers \( c \) that satisfy the conclusion of the Mean Value Theorem.** (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).
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