Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Maximization
Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.
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Why does Newton's method fail at all of these points in the graph except for x=5, especially when comparing x=3 versus x=5?

+ 1 3 (a) X1 = 0 Newton's method succeeds. Newton's method fails. (b) X1 = 1 Newton's method succeeds. Newton's method fails. (c) x1 = 3 Newton's method succeeds. Newton's method fails. (d) X1 = 4 Newton's method succeeds. Newton's method fails. (e) x1 = 5 Newton's method succeeds. Newton's method fails.
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Transcribed Image Text:+ 1 3 (a) X1 = 0 Newton's method succeeds. Newton's method fails. (b) X1 = 1 Newton's method succeeds. Newton's method fails. (c) x1 = 3 Newton's method succeeds. Newton's method fails. (d) X1 = 4 Newton's method succeeds. Newton's method fails. (e) x1 = 5 Newton's method succeeds. Newton's method fails.
Expert Solution
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Step 1

Since the graph cut at two point.

at x=2, x=6

and graph never touch the  negative x-axis.

and tangent parallel to the x-axis at x=1 and x=4

 

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