For f(x)=√x over the interval [0, 9], verify that f satisfies the hypothesis of the Mean Value Theorem, and therefore there exists at least one value c € (0,9) such that f'(c) is equal to the slope of the line connecting (0, f(0)) and (9, f(9)). Find the value c guaranteed by the Mean Value Theorem. Enter the value as a decimal number. Answer:
For f(x)=√x over the interval [0, 9], verify that f satisfies the hypothesis of the Mean Value Theorem, and therefore there exists at least one value c € (0,9) such that f'(c) is equal to the slope of the line connecting (0, f(0)) and (9, f(9)). Find the value c guaranteed by the Mean Value Theorem. Enter the value as a decimal number. Answer:
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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![For \( f(x) = \sqrt{x} \) over the interval \([0, 9]\), verify that \( f \) satisfies the hypothesis of the Mean Value Theorem, and therefore there exists at least one value \( c \in (0, 9) \) such that \( f'(c) \) is equal to the slope of the line connecting \((0, f(0))\) and \((9, f(9))\). Find the value \( c \) guaranteed by the Mean Value Theorem. Enter the value as a decimal number.
Answer: [ ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34042937-5f53-43cf-ac4b-3f6d98d86f6b%2Fe1b83173-620d-4f01-a097-bd5434659156%2Fmu89w8b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For \( f(x) = \sqrt{x} \) over the interval \([0, 9]\), verify that \( f \) satisfies the hypothesis of the Mean Value Theorem, and therefore there exists at least one value \( c \in (0, 9) \) such that \( f'(c) \) is equal to the slope of the line connecting \((0, f(0))\) and \((9, f(9))\). Find the value \( c \) guaranteed by the Mean Value Theorem. Enter the value as a decimal number.
Answer: [ ]
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