Explanation Given information: The function is as, f ( x ) = sin x Concept used: If the function f ( x ) is continuous and differentiable on the interval [ a , b ] and the value of f ( a ) and f ( b ) are equal as f ( a ) = f ( b ) then the number c lies on the interval such that f ′ ( c ) = 0 . Calculation: The given function f ( x ) is the sinusoidal function. Substitute π 4 for x in the equation (1) to obtain the value of f ( π 4 ) . f ( π 4 ) = sin π 4 = 1 2 Substitute 3π 4 for x in the equation (1) to obtain the value of f ( 3π 4 ) . f ( 3π 4 ) = sin 3π 4 = 1 2 The value of the function at x = π 4 and x = 3π 4 is 1 2 and 1 2 respectively. f ( π 4 ) = f ( 3π 4 ) Therefore, the value of the function at endpoints on the interval [ π 4 , 3π 4 ] is same such that the Rolle’s Theorem is verified

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4.2, Problem 58E

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To find:

The value of c for the function f(x)=sinx on the interval [π4,3π4] such that f′(c)=0 and verify Rolle’s Theorem.

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Chapter 4.2, Problem 57E

Chapter 4.2, Problem 59E

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Chapter 4 Solutions

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Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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The value of c for the function f ( x ) = sin x on the interval [ π 4 , 3π 4 ] such that f ′ ( c ) = 0 and verify Rolle’s Theorem.

Solution Summary: The author explains how the function f(x)=mathrmsinx is a sinusoidal function.

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To find:

The value of c for the function f(x)=sinx on the interval [π4,3π4] such that f′(c)=0 and verify Rolle’s Theorem.

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Chapter 4 Solutions

The value of c for the function f ( x ) = sin x on the interval [ π 4 , 3π 4 ] such that f ′ ( c ) = 0 and verify Rolle’s Theorem.

Solution Summary: The author explains how the function f(x)=mathrmsinx is a sinusoidal function.

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To find: The value of c for the function f(x)=sinx on the interval [π4,3π4] such that f′(c)=0 and verify Rolle’s Theorem.

Want to see the full answer?

Chapter 4 Solutions

To find:

The value of c for the function f(x)=sinx on the interval [π4,3π4] such that f′(c)=0 and verify Rolle’s Theorem.