Explanation Given: The given function is f ( x ) = sin x ; [ a , b ] = [ 0 , π 2 ] Calculation: Since, the function is continuous and differentiable at c ∈ [ 0 , π 2 ] Therefore, using Mean Value Theorem; f ' ( c ) = f ( 0 ) − f ( π 2 ) π 2 − 0 f ' ( c ) = sin ( π 2 ) − sin ( 0 ) π 2 f ' ( c ) = 1 −<

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Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 3.1, Problem 59S

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The reason why the given function ‘f’ satisfies the hypothesis of the Mean Value Theorem on the given interval [a, b] and the exact values c∈(a,b) which satisfies the conclusion of the Mean Value Theorem

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Chapter 3.1, Problem 58S

Chapter 3.1, Problem 60S

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Chapter 3 Solutions

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Ch. 3.1 - Prob. 1TB Ch. 3.1 - Prob. 0C Ch. 3.1 - Prob. 1C Ch. 3.1 - Prob. 2C Ch. 3.1 - Prob. 3C Ch. 3.1 - Prob. 4C Ch. 3.1 - Prob. 5C Ch. 3.1 - Prob. 6C Ch. 3.1 - Prob. 7C Ch. 3.1 - Prob. 8C

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The reason why the given function ‘f’ satisfies the hypothesis of the Mean Value Theorem on the given interval [a, b] and the exact values c ∈ ( a , b ) which satisfies the conclusion of the Mean Value Theorem

Solution Summary: The author explains that the function satisfies the hypothesis of the Mean Value Theorem on the given interval and the exact values cin (a,b).

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The reason why the given function ‘f’ satisfies the hypothesis of the Mean Value Theorem on the given interval [a, b] and the exact values c∈(a,b) which satisfies the conclusion of the Mean Value Theorem

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Chapter 3 Solutions