Explanation Given: The given function is: f ( x ) = x ln x Consider the function: f ( x ) = x ln x For finding roots of the function; f (x)=0 x ln x = 0 Either x = 0 or ln x = 0 x = 0 , 1 The first derivative of the function is given below: f ' ( x ) = d d x ( x ln x ) = x . 1 x + ln x .1 = 1 + ln x This derivative is always defined and continuous for x > 0, so the critical points of f are just the places where f ' (x)=0; that is 1 + ln x = 0 ln x = − 1 x = e − 1 Now, f ( 1 e ) = 1 e ( ln 1 e ) = − 1 e Therefore, the local minimum at x= − 1 e

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 3, Problem 13SC

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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 12SC

Chapter 3, Problem 14SC

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Chapter 3 Solutions

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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. The function has no local maximum and a local minimum.

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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