Explanation Given: The given function is f ( x ) = cos x , [ a , b ] = [ − π 2 , 3 π 2 ] 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 ( − π 2 ) = cos ( − π 2 ) = 0 An

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Question

Chapter 3.1, Problem 45S

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 44S

Chapter 3.1, Problem 46S

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Chapter 3 Solutions

Calculus

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ACP Ch. 3 - Prob. BCP Ch. 3 - Prob. CCP Ch. 3 - Prob. DCP

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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 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 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.