Explanation Given information: f ( x ) = x − ln x , x > 0 Fact used: If f ' changes from negative to positive at p, then f has a local minimum at p. f ' changes from positive to negative at p, then f has a local maximum at p. Calculation: f ( x ) = x − ln x , x > 0 (Given) Differentiating with respect to ‘x’, we get f ' ( x ) = 1 − 1 x Equating f ' ( x ) = 0 ⇒ 1 − 1 x = 0

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 4.3, Problem 44P

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The exact global maximum and minimum values of the function f(x)=x−lnx,x>0.

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Chapter 4.3, Problem 43P

Chapter 4.3, Problem 45P

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The exact global maximum and minimum values of the function f ( x ) = x − ln x , x > 0 .

Solution Summary: The author explains the global minimum and minimum values of the function f(x)=x-mathrmlnx,x>0.

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To find:

The exact global maximum and minimum values of the function f(x)=x−lnx,x>0.

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Chapter 4 Solutions

The exact global maximum and minimum values of the function f ( x ) = x − ln x , x &gt; 0 .

Solution Summary: The author explains the global minimum and minimum values of the function f(x)=x-mathrmlnx,x>0.

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To find: The exact global maximum and minimum values of the function f(x)=x−lnx,x>0.

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Chapter 4 Solutions

The exact global maximum and minimum values of the function f ( x ) = x − ln x , x > 0 .

To find:

The exact global maximum and minimum values of the function f(x)=x−lnx,x>0.