Explanation Given: The given function is: f ( x ) = e x 1 − e x Consider the function: f ( x ) = e x 1 − e x For finding roots of the function; f(x)=0 e x 1 − e x = 0 e x = 0 [multiplying both sides by 1-e x ] x = − ∞ The first derivative of the function is given below: f ' ( x ) = d d x ( e x 1 − e x ) = ( 1 − e x ) e x − e x ( − e x ) ( 1 − e x ) 2 = e x − e 2 x + e 2 x ( 1 − e x ) 2 = e x ( 1 − e x ) 2 Again for second derivative is given by f " ( x ) = d d x e x ( 1 − e x ) 2 = ( 1 − e x ) 2 e x − e x

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3, Problem 15SC

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To determine all roots, local maxima, minima and inflection points of each function f and also determine whether any local extrema are also global extrema on the domain of f.

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Chapter 3, Problem 14SC

Chapter 3, Problem 16SC

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all roots, local maxima, minima and inflection points of each function f and also determine whether any local extrema are also global extrema on the domain of f.

Solution Summary: The author explains the function's roots, local maxima, minima and inflection points, and determines whether any local extrema are also global Extrema on the domain of f.

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To determine all roots, local maxima, minima and inflection points of each function f and also determine whether any local extrema are also global extrema on the domain of f.

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Chapter 3 Solutions