Explanation The provided function is: f ( x ) = x e − x . Formula used: Write the formula for derivative of power rule. If f ( x ) = x n for any number n , then the derivative. f ′ ( x ) = n x n − 1 If f ( x ) = k for any real number k , then the derivative is defined by the formula. f ′ ( x ) = 0 Write the formula for derivative of exponents. f ( x ) = e n x for any number n , then the derivative. f ′ ( x ) = n e n x Calculation: Consider the following expression. f ( x ) = x e − x Differentiate the above expression. f ′ ( x ) = e − x − x e − x Differentiate the above expression. f ″ ( x ) = − e − x − ( e − x + x e − x ) = − 2 e − x + x e − x Substitute 0 for x

Mathematics with Applications, Books a la Carte, and MyLab Math with Pearson eText - Title-Specific Access Card Package (12th Edition)

12th Edition

ISBN: 9780134862651

Author: Lial

Publisher: PEARSON

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Chapter 12.2, Problem 15E

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To calculate: the second derivative of f(x)=xe−x and determine f″(0), f″(2) and f″(−3)

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Chapter 12.2, Problem 8E

Chapter 12.2, Problem 16E

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Mathematics with Applications, Books a la Carte, and MyLab Math with Pearson eText - Title-Specific Access Card Package (12th Edition)

Ch. 12.1 - Checkpoint 1 For what values of x is the function...Ch. 12.1 - Checkpoint 2 Find all intervals on which is...Ch. 12.1 - Checkpoint 3 Identity the x-values of all points...Ch. 12.1 - Checkpoint 4 Find the critical numbers for each of...Ch. 12.1 - Prob. 5CP Ch. 12.1 - Prob. 6CP Ch. 12.1 - Checkpoint 7 Find the locations of the local...Ch. 12.1 - Prob. 8CP Ch. 12.1 - Checkpoint 9 If a sales function is given by...Ch. 12.1 - Prob. 1E

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the second derivative of f ( x ) = x e − x and determine f ″ ( 0 ) , f ″ ( 2 ) and f ″ ( − 3 )

Solution Summary: The author explains the formula for derivative of power rule.

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To calculate: the second derivative of f(x)=xe−x and determine f″(0), f″(2) and f″(−3)

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Chapter 12 Solutions