Explanation Given: y = f ( x ) = x ( x − 2 ) 3 We know that the critical points are the points at which the derivatives of the function become zero or undefined. Here, the given function is y = f ( x ) = x ( x − 2 ) 3 Differentiating the above function with respect to x, we get f ' ( x ) = d d x ( x ( x − 2 ) 3 ) = x .3 ( x − 2 ) 2 + ( x − 2 ) 3 .1 = ( 4 x − 2 ) + ( x − 2 ) 2 To find out the critical points, we equate the above equation to zero. i.e. f ' ( x ) = 0 i.e

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.3, Problem 30E

To determine

To find all the critical points of the function y=x(x−2)3 and the intervals on which the function is increasing or decreasing. Also determine the critical point is a local minimum or maximum.

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Chapter 4.3, Problem 29E

Chapter 4.3, Problem 31E

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To find all the critical points of the function y = x ( x − 2 ) 3 and the intervals on which the function is increasing or decreasing. Also determine the critical point is a local minimum or maximum.

Solution Summary: The author explains that the critical points are the points at which the derivatives of the function become zero or undefined.

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To find all the critical points of the function y=x(x−2)3 and the intervals on which the function is increasing or decreasing. Also determine the critical point is a local minimum or maximum.

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Chapter 4 Solutions