Explanation Given expression f x = x 2 - 2 x 2 - 2 can be derivated by the following rules. Definition of the Product Rule: If f ( x ) = u ( x ) · v ( x ) , and if u ' x and v ' x both exist, then f ' x = u ( x ) · v ' x + v ( x ) · u ' x . The derivative of a product of two functions is the first functions times the derivative of the second plus the second function times the derivative of the first. Based on the above product rule, Let us consider u ( x ) = x 2 - 2 v ( x ) = x 2 - 2 According to Power Rule and Constant Rule u ' x and v ' x can be written as below, u ' x = ( 2 ) ( x 2 - 1 ) - 0 u ' x = ( 2 ) ( x 1 ) u ' x = 2 x Similarly, v ' x = = ( 2 ) ( x 2 - 1 ) - 0 v ' x = 2 x 1 = 2 x Substituting u ' x = 2 x , v ' x = 2 x , u ( x ) = ( x 2 - 2 ) and v ( x ) = x 2 - 2 in the below function, f ' x = u ( x ) · v ' x + v ( x ) · u ' x . f ' x = ( x 2 - 2 ) · 2 x + ( x 2 - 2 ) · 2 x

2nd Edition

ISBN: 9780321964038

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

Publisher: Pearson Addison Wesley,

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Chapter 4.2, Problem 39E

To determine

To find:

The value(s) of x in which f'x=0, where fx=x2-2x2-2.

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Chapter 4.2, Problem 38E

Chapter 4.2, Problem 40E

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