Explanation Given : The function is f ( x ) = ( ln x ) 2 + 1 . Calculation: Derivate the function with respect to x as follows: d d x f ( x ) = d d x ( ( ln x ) 2 + 1 ) f ′ ( x ) = 2 log x x For increasing interval of the function, f ′ ( x ) > 0 2 log x x > 0 x ∈ ( 1 , ∞ ) The sign chart is as follows: For decreasing interval of the function, f ′ ( x ) < 0 2 log x x < 0 x ∈ ( 0 , 1 ) The sign chart is shown below:

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.3, Problem 81S

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To sketch: The graph of the function f(x)=(lnx)2+1 .

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Chapter 3.3, Problem 80S

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The graph of the function f ( x ) = ( ln x ) 2 + 1 .

Solution Summary: The author illustrates the graph of the function f(x)= (mathrmlnx

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To sketch: The graph of the function f(x)=(lnx)2+1 .

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