Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![The image contains a question about the Mean Value Theorem in calculus. It asks for the value of \( c \) that satisfies the theorem on the interval \([0, 5]\) for the function \( f(x) = x^3 - 6x \).
Options for the value of \( c \) are provided:
- \(\frac{5}{\sqrt{3}}\) (this option is selected)
- 1
- \(\frac{5}{3}\)
- 0
The question requires applying the Mean Value Theorem, which states that if a function \( f \) is continuous on the closed interval \([a, b]\) and differentiable on the open interval \((a, b)\), then there exists at least one number \( c \) in \((a, b)\) such that:
\[
f'(c) = \frac{f(b) - f(a)}{b - a}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e71e459-267b-4c65-984a-67009d5ae993%2F0396de09-48a0-4a13-a5cf-9677d8567b63%2Fxq8irh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a question about the Mean Value Theorem in calculus. It asks for the value of \( c \) that satisfies the theorem on the interval \([0, 5]\) for the function \( f(x) = x^3 - 6x \).
Options for the value of \( c \) are provided:
- \(\frac{5}{\sqrt{3}}\) (this option is selected)
- 1
- \(\frac{5}{3}\)
- 0
The question requires applying the Mean Value Theorem, which states that if a function \( f \) is continuous on the closed interval \([a, b]\) and differentiable on the open interval \((a, b)\), then there exists at least one number \( c \) in \((a, b)\) such that:
\[
f'(c) = \frac{f(b) - f(a)}{b - a}
\]
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