Explanation Given: The given function is f ( x ) = 2 1 − ln x Concept used: A function f ( x ) has its critical points or extreme points for f ′ ( x ) = 0 . The function has its maximum or largest value for f ′ ′ ( x ) < 0 . The function has its minimum or least value for f ′ ′ ( x ) > 0 . Calculation: Consider the given function. f ( x ) = 2 1 − ln x The differentiation of the function is given by f ′ ( x ) = − 2 1 − ln x x ln 2 For critical point of the function, consider f ′ ( x ) = 0 − 2 1 − ln x x ln 2 = 0 2 1 − ln x = 0 ln x = ∞ x = 0 Now, for extreme values of the function, construct the second derivative

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Question

Chapter 3.1, Problem 34S

To determine

The critical points of the given function.

Whether the function has local minimum, local maximum or none of the two using a graph utility.

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Chapter 3.1, Problem 33S

Chapter 3.1, Problem 35S

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Chapter 3 Solutions

Calculus

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The critical points of the given function. Whether the function has local minimum , local maximum or none of the two using a graph utility.

Solution Summary: The author analyzes the critical points of the given function using a graph utility.

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The critical points of the given function.

Whether the function has local minimum, local maximum or none of the two using a graph utility.

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Chapter 3 Solutions

The critical points of the given function. Whether the function has local minimum , local maximum or none of the two using a graph utility.

Solution Summary: The author analyzes the critical points of the given function using a graph utility.

Concept explainers

Videos

The critical points of the given function. Whether the function has local minimum, local maximum or none of the two using a graph utility.

Want to see the full answer?

Chapter 3 Solutions

The critical points of the given function.

Whether the function has local minimum, local maximum or none of the two using a graph utility.