Explanation Given: y = 8 x 2 − x 4 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 = 8 x 2 − x 4 Differentiating the above function, we get d y d x = 16 x − 4 x 3 To find out the critical points, we equate the above equation to zero. i.e. 16 x − 4 x 3 = 0 On solving this, we get x = − 2 , x = 0 and x = 2 Therefore, the critical points of the given functionoccur at x = − 2 , x = 0 and x = 2 . Now we second derivative to find the inflection points. d 2 y d x 2 = 16 − 12 x 2 To find out the inflection points, we equate the above equation to zero. 16 − 12 x 2 = 0 On solving the above equation, we obtain x = − 2 3 3 and x = 2 3 3

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ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4, Problem 48CRE

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To find the points of inflection for the function, y=8x2−x4.

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Chapter 4, Problem 47CRE

Chapter 4, Problem 49CRE

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To find the points of inflection for the function, y = 8 x 2 − x 4 .

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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