Explanation Given: The given function is f ( x ) = − x 3 + 3 x 2 − 7 ; [ a , b ] = [ − 2 , 3 ] Calculation: Since, the function is continuous and differentiable at c ∈ [ − 2 , 3 ] Therefore, using Mean Value Theorem; f ' ( c ) = f ( 3 ) − f ( − 2 ) b − a f ' ( c ) = − 3 3 + 3 ⋅ 3 2 − 7 − [ − ( − 2 ) 3 + 3 ⋅ ( − 2 ) 2 − 7 ] 3 − ( − 2 ) f ' (

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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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

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Chapter 3.1, Problem 54S

Chapter 3.1, Problem 56S

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Chapter 3 Solutions

Calculus

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.

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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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