Explanation Given: function f ( x ) = x ln x . Calculation: Find critical values by finding f ′ ( x ) as: f ( x ) = x ln x f ′ ( x ) = ln ( x ) + 1 Find the roots of f ′ ( x ) : ln ( x ) + 1 = 0 x = 1 e = 0.3679 x = 0.3679 The critical value is 0.3679, which we will use to divide the a-axis into four intervals on the sign chart, the intervals are ( − ∞ , 0.3679 ) and ( 0.3679 , ∞ ) . Next find the sign of the derivative in each interval taking the value in each interval as: f ′ ( x ) = ln ( x ) + 1 x = − 1 , f ′ ( − 1 ) = ln ( − 1 ) + 1 = N o s o l u t i o n x = 1 , f ′ ( 1 ) = ln ( 1 ) + 1 = 1 x = 2 , f ′ ( 1 ) = ln ( 2 ) + 1 = 1

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ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 3.2, Problem 75S

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Chapter 3.2, Problem 74S

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Chapter 3 Solutions

Calculus

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Chapter 3 Solutions