Explanation Given Information: The provided function is f ( x ) = x − l n x 2 and the domain is ( 0 , + ∞ ) . Calculation: Consider the provided function, f ( x ) = x − l n x 2 Differentiate both sides of the above equation with respect to x , f ′ ( x ) = 1 − 2 x x 2 f ′ ( x ) = 1 − 2 x Locating stationary points: Stationary Points: Points in the interior of the domain where the derivative of the function is zero. To locate stationary points set f ′ ( x ) = 0 and solve for x . So, f ′ ( x ) = 0 1 − 2 x = 0 Add 2 x to both sides of the above equation, 1 − 2 x = 0 1 − 2 x + 2 x = 2 x 1 = 2 x Multiply both sides by x , 1 = 2 x x = 2 The function f ′ ( x ) = 0 for x = 2 . Therefore, the stationary point of the function f ( x ) = x − l n x 2 is x = 2 . Locating Singular points: Singular Points: Points in the interior of the domain where the derivative of the function is not defined. To locate singular points, find the interior points x where f ′ ( x ) is not defined but f ( x ) is defined. The function f ′ ( x ) = 1 − 2 x is not defined for x = 0 and it is not in the domain

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

7th Edition

ISBN: 9781337275972

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

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Chapter 12.1, Problem 38E

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To calculate: The exact location of the relative and absolute extrema of the function f(x)=x−lnx2 with the domain (0,+∞).

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Chapter 12.1, Problem 37E

Chapter 12.1, Problem 39E

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Chapter 12 Solutions

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

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The exact location of the relative and absolute extrema of the function f ( x ) = x − l n x 2 with the domain ( 0 , + ∞ ) .

Solution Summary: The author calculates the exact location of the relative and absolute extrema of a function with the domain (0,+infty

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To calculate: The exact location of the relative and absolute extrema of the function f(x)=x−lnx2 with the domain (0,+∞).

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Chapter 12 Solutions