1. Numerical Methods Newton’s Method for One -Dimensional Optimization - Example

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5. 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.

6. Solution The function to be maximized is
Iteration 1: Use as the initial estimate of the solution

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

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11. The End - Really