Explanation Given: The given function is f ( x ) = x 3 − 2 x + 1 ; [ a , b ] = [ 0 , 6 ] Calculation: Since, the function is continuous and differentiable at c ∈ [ 0 , 6 ] Therefore, using Mean Value Theorem; f ' ( c ) = f ( b ) − f ( a ) b − a f ' ( c ) = 6 3 − 2 ⋅ 6 + 1 − ( 0 3 − 2 ⋅ 0 + 1 )

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.1, Problem 54S

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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 53S

Chapter 3.1, Problem 55S

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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 [a, b] and the exact values.

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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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