A line segment extends horizontally to the left from the point and another line segment

Chapter 12, Problem 78

(choose chapter or problem)

A line segment extends horizontally to the left from the point (-1, -1), and another line segment extends horizontally to the right from the point (1, 1) as shown in the figure. Find a curve of the form

\(y=a x^{5}+b x^{3}+c x\)

that connects the points (-1, -1) and (1, 1) so that the slope and curvature of the curve are zero at the endpoints.

                                             

Text Transcription:

y = ax^5 + bx^3 + cx

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