Explanation Given: y = f ( x ) = x 5 + x 3 + 1 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 5 + x 3 + 1 Differentiating the above function with respect to x, we get f ' ( x ) = d d x ( x 5 + x 3 + 1 ) = 5 x 4 + 3 x 2 = x 2 ( 5 x 2 + 3 ) To find out the critical points, we equate the above equation to zero. i.e. f ' ( x ) = 0 i.e

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4.3, Problem 35E

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To find all the critical points of the function y=x5+x3+1 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 34E

Chapter 4.3, Problem 36E

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To find all the critical points of the function y = x 5 + x 3 + 1 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=x5+x3+1 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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