Explanation Given: y = x ( x 2 − 4 ) ( 2 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 ) ( 2 3 ) Differentiating the above function, we get d y d x = 1 × ( x 2 − 4 ) ( 2 3 ) − 4 x 3 x 2 − 4 3 [ ( x 2 − 4 ) ( 2 3 ) ] 2 = − x 2 − 12 3 ( x 2 − 4 ) ( 5 3 ) To find out the critical points, we equate the above equation to zero. i.e. − x 2 − 12 3 ( x 2 − 4 ) ( 5 3 ) = 0 There is no solution for the above and hence there are nocritical pointsfor the given function. Now we second derivative to find the inflection points

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4, Problem 52CRE

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Chapter 4 Solutions

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To find the points of inflection for the function, y = x ( x 2 − 4 ) ( 2 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)(23).

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