Explanation Given: Function is f ( x ) = x 2 − 8 ln ( x ) and specified domain is [ 1 , 4 ] . Approach: Steps for calculating absolute extrema in given interval are given below: Find critical numbers of function in given interval. (Critical numbers are that values where f ' ( x ) = 0 ). Evaluate the value of function at each critical point. Evaluate the value of function at end point of the interval. The largest value is absolute maximum and smallest value is absolute minimum. Calculation: Given function is f ( x ) = x 2 − 8 ln ( x ) . On differentiating with respect to x f ' ( x ) = d d x ( x 2 − 8 ln ( x ) ) = 2 x − 8 × 1 x = 2 x 2 − 8 x For critical values we can make derivative equal to zero. f ' ( x ) = 0 2 x 2 − 8 x = 0 2 x 2 − 8 = 0 x 2 = 4 x = ± 2 We can also get critical points where derivative is undefined

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 6.1, Problem 25E

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To find:

Value of all extrema for the given function f(x)=x2−8ln(x) in a specified domain [1,4] if exists.

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Chapter 6.1, Problem 24E

Chapter 6.1, Problem 26E

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Value of all extrema for the given function f ( x ) = x 2 − 8 ln ( x ) in a specified domain [ 1 , 4 ] if exists.

Solution Summary: The author explains the steps for calculating absolute extrema in a given interval.

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To find:

Value of all extrema for the given function f(x)=x2−8ln(x) in a specified domain [1,4] if exists.

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Chapter 6 Solutions

Value of all extrema for the given function f ( x ) = x 2 − 8 ln ( x ) in a specified domain [ 1 , 4 ] if exists.

Solution Summary: The author explains the steps for calculating absolute extrema in a given interval.

Concept explainers

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To find: Value of all extrema for the given function f(x)=x2−8ln(x) in a specified domain [1,4] if exists.

Want to see the full answer?

Chapter 6 Solutions

To find:

Value of all extrema for the given function f(x)=x2−8ln(x) in a specified domain [1,4] if exists.