Explanation Given: y = x ( x 2 − 4 ) 1 / 3 Formula Used: Calculation: We know that the inflection points are the points at which the sign of the second derivatives of the function changes. Here, the given function is y = x ( x 2 − 4 ) 1 / 3 Differentiating the above function, we get d y d x = x 2 − 12 3 ( x 2 − 4 3 ) 2 ( x 2 − 4 ) 2 3 To find out the critical points, we equate the above equation to zero. i.e. x 2 − 12 3 ( x 2 − 4 3 ) 2 ( x 2 − 4 ) 2 3 = 0 On solving this, we get x = − 2 3 and x = + 2 3 Therefore, the critical point of the given functionoccursat x = − 2 3 and x = + 2 3 . Now we second derivative to find the inflection points. d 2 y d x 2 = d d x [ x 2 − 12 3 ( x 2 − 4 3 ) 2 ( x 2 − 4 ) 2 3 ] To find out the inflection points, we equate the above equation to zero

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4, Problem 44CRE

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To find the points of inflection for the function, y=x(x2−4)1/3.

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To find the points of inflection for the function, y = x ( x 2 − 4 ) 1 / 3 .

Solution Summary: The author explains that the inflection points are the points at which the sign of the second derivatives of a function changes.

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To find the points of inflection for the function, y=x(x2−4)1/3.

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