anonymous
  • anonymous
Given any arbitrary hyper-ellipsoid defined by an orthonormal basis, center and extents along each axis, calculate the global maximum of the curve bounded by any arbitrary vector V, and the perpendicular plane P to V, where both V and P intersect the each other and the hyper-ellipsoid.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Do you know the standard equation of the ellipsoid? .. that will help.
anonymous
  • anonymous
So I should implicitly differentiate the bounded curve of the equation of an ellipsoid to find the maximum? What about its arbitrary orientation?
anonymous
  • anonymous
First you setup the ellipsoid from the conditions, then find critical points based on D=f_xx*f_yy-f_xy*f_yx, D>0 where f_xx>0. Then put each critical point, plus the end points into the original ellipsoid to the greatest value, which is the global maximum.

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