Numerical Methods Newton’s Method for One -Dimensional Optimization - Example http://nm.mathforcollege.com http://nm.mathforcollege.com.

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Numerical Methods Newton’s Method for One -Dimensional Optimization - Example http://nm.mathforcollege.com http://nm.mathforcollege.com

For more details on this topic Go to http://nm.mathforcollege.com Click on Keyword Click on Newton’s Method for One-Dimensional Optimization

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Example . 2 2   2 The cross-sectional area A of a gutter with equal base and edge length of 2 is given by Find the angle  which maximizes the cross-sectional area of the gutter. http://nm.mathforcollege.com

Solution The function to be maximized is Iteration 1: Use as the initial estimate of the solution http://nm.mathforcollege.com

Solution Cont. Iteration 2: Summary of iterations  1 0.7854 2.8284 -10.8284 1.0466 5.1962 2 0.0062 -10.3959 1.0472 3 1.06E-06 -10.3923 4 3.06E-14 5 1.3322E-15 Remember that the actual solution to the problem is at 60 degrees or 1.0472 radians. http://nm.mathforcollege.com

The End http://nm.mathforcollege.com

Acknowledgement This instructional power point brought to you by Numerical Methods for STEM undergraduate http://nm.mathforcollege.com Committed to bringing numerical methods to the undergraduate

For instructional videos on other topics, go to http://nm.mathforcollege.com This material is based upon work supported by the National Science Foundation under Grant # 0717624. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

The End - Really