Explanation Given: The given function is f ( x ) = arctan ( x ) Concept Used: 1. Critical points are the points in the domain of the function where the derivative of the function is equal to zero or the derivative does not exist. 2. Second derivative test: If x = c is a critical number of f at which f ″ is defined, then If f ′ ′ ( c ) > 0 , then f has relative minima at x = c . If f ′ ′ ( c ) < 0 , then f has relative maxima at x = c . Calculation: To determine the local extrema of function f ( x ) = arctan ( x ) , first find the critical points, for that find the derivative of the function as, f ′ ( x ) = d d x [ arctan ( x ) ] = 1 1 + x 2 Now find the points where f ′ ( x ) = 0 or f ′ ( x ) does not exist

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 3.3, Problem 37S

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To determine the local extrema of function f(x)=arctan(x) using second-derivative test. And verify the answer using graphing utility.

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Chapter 3.3, Problem 36S

Chapter 3.3, Problem 38S

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Chapter 3 Solutions

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the local extrema of function f ( x ) = arctan ( x ) using second-derivative test. And verify the answer using graphing utility.

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To determine the local extrema of function f(x)=arctan(x) using second-derivative test. And verify the answer using graphing utility.

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Chapter 3 Solutions