21.X. Find the dimensions of the box of maximum volume which can be fitted into the ellipsoid 1, c2 assuming that each edge of the box is parallel to a coordinate axis. + +

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Help with exercise 21.W and 21.X

Demonstrate step by step, so that you can understand the proof, please (mentioning the definitions used)

21.W. Show that the function
f(i, n) = (n – *) (n – 25*)
does not have a relative extremum at 0 = (0, 0) although it has a relative
minimum along every line = at, n = ßt.
21.X. Find the dimensions of the box of maximum volume which can be
fitted into the ellipsoid
to
1,
assuming that each edge of the box is parallel to a coordinate axis.
+
Transcribed Image Text:21.W. Show that the function f(i, n) = (n – *) (n – 25*) does not have a relative extremum at 0 = (0, 0) although it has a relative minimum along every line = at, n = ßt. 21.X. Find the dimensions of the box of maximum volume which can be fitted into the ellipsoid to 1, assuming that each edge of the box is parallel to a coordinate axis. +
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