Explanation Given Information: The function is y = x e x . Formula used: If f ( x ) = c ⋅ u ( x ) , where, c is a constant and u ( x ) is a differentiable function of x , then, f ′ ( x ) = c ⋅ u ′ ( x ) According to the property of derivatives, if y = e x , where, u is a differentiable function of x , d y d x = e x According to the power rule of differentiation, d y d x = n x n − 1 According to the quotient rule of derivatives, d d x ( f g ) = g f ′ − f g ′ g 2 Calculation: Consider the provided function, y = x e x To find the relative minimum, differentiate both sides with respect to x , d y d x = d d x ( x e x ) = d d x ( x e x ) Apply the quotient rule for derivatives, d y d x = ( e x ) ⋅ ( d d x ( x ) ) − x ⋅ ( d d x ( e x ) ) ( e x ) 2 Simplify the derivative using the quotient rule of derivatives, d y d x = ( e x ) ⋅ ( x 1 − 1 ) − x ⋅ ( e x ) e 2 x = e x − x e x e 2 x Take e x common from the numerator, d y d x = e x ( 1 − x ) e 2 x = 1 − x e x To calculate the value of mean, the value of d y d z should be equal to zero

Mathematical Applications for the Management, Life, and Social Sciences

11th Edition

ISBN: 9781305108042

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 11.2, Problem 40E

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To calculate: The relative maxima or minima for the function, y=xex.

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Chapter 11.2, Problem 39E

Chapter 11.2, Problem 41E

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Chapter 11 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 11.1 - 1. Ch. 11.1 - 2. If Ch. 11.1 - Prob. 3CP Ch. 11.1 - 4. Find . Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Find the derivatives of the functions in Problems...

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The relative maxima or minima for the function, y = x e x .

Solution Summary: The author calculates the relative maxima or minima for the function, y=xe

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To calculate: The relative maxima or minima for the function, y=xex.

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Chapter 11 Solutions