Explanation Given: The function is given as: f ( x ) = 1 + x + x 2 x 2 + x − 2 Evaluating the derivative of the function using the quotient rule : f ' ( x ) = d d x ( 1 + x + x 2 x 2 + x − 2 ) = ( x 2 + x − 2 ) ( 1 + 2 x ) − ( 1 + x + x 2 ) ( 2 x + 1 ) ( x 2 + x − 2 ) 2 = ( 1 + 2 x ) ( x 2 + x − 2 − 1 − x − x 2 ) ( x 2 + x − 2 ) 2 = − 3 ( 1 + 2 x ) ( x 2 + x − 2 ) 2 The derivative is defined and continuous everywhere except at x=1,-2 so the critical points of f are just the points where f ' ( x ) = 0

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Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 3.2, Problem 41S

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The local extrema of the given function and then verifying the algebraic answer with the graphs.

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Chapter 3.2, Problem 40S

Chapter 3.2, Problem 42S

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Chapter 3 Solutions

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The local extrema of the given function and then verifying the algebraic answer with the graphs.

Solution Summary: The author explains the local extrema of the given function and then verifying the algebraic answer with the graphs. The derivative is defined and continuous everywhere except at x=1,-2.

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Chapter 3 Solutions