Explanation Given: The given function is f ( x ) = sin 2 x , [ a , b ] = [ 0 , 2 π ] Concept used: Rolle’s Theorem: A function f ( x ) is continuous on [ a , b ] A function f ( x ) is differentiable on ( a , b ) f ( a ) = f ( b ) Then the function f ( x ) satisfies all conditions of Rolle’s theorem and then there exist a value c ∈ ( a , b ) such that f ′ ( c ) = 0 Calculation: Since f ( x ) is trigonometric function; therefore, f ( x ) is continuous and differentiable for everywhere Now, f ( 0 ) = sin 2 ( 0 ) = sin 0 = 0 And f

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Question

Chapter 3.1, Problem 46S

To determine

Whether the given function satisfies the hypothesis of Rolle’s Theorem on the given interval

[a,b] . The exact values of all c∈(a,b) that satisfy the conclusion of Rolle’s Theorem.

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Chapter 3.1, Problem 45S

Chapter 3.1, Problem 47S

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Chapter 3 Solutions

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Whether the given function satisfies the hypothesis of Rolle’s Theorem on the given interval [ a , b ] . The exact values of all c ∈ ( a , b ) that satisfy the conclusion of Rolle’s Theorem.

Solution Summary: The author explains how the function satisfies the hypothesis of Rolle’s Theorem on the given interval left[a,bright]

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Whether the given function satisfies the hypothesis of Rolle’s Theorem on the given interval

[a,b] . The exact values of all c∈(a,b) that satisfy the conclusion of Rolle’s Theorem.

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Chapter 3 Solutions

Whether the given function satisfies the hypothesis of Rolle’s Theorem on the given interval [ a , b ] . The exact values of all c ∈ ( a , b ) that satisfy the conclusion of Rolle’s Theorem.

Solution Summary: The author explains how the function satisfies the hypothesis of Rolle’s Theorem on the given interval left[a,bright]

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Whether the given function satisfies the hypothesis of Rolle’s Theorem on the given interval [a,b] . The exact values of all c∈(a,b) that satisfy the conclusion of Rolle’s Theorem.

Want to see the full answer?

Chapter 3 Solutions

Whether the given function satisfies the hypothesis of Rolle’s Theorem on the given interval

[a,b] . The exact values of all c∈(a,b) that satisfy the conclusion of Rolle’s Theorem.