Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid 9 - y² 36 + 25 1 Hint: By symmetry, you can restrict your attention to the first octant (where x, y, z ≥ 0), and assume your volume has the form V 8xyz. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume: =
Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid 9 - y² 36 + 25 1 Hint: By symmetry, you can restrict your attention to the first octant (where x, y, z ≥ 0), and assume your volume has the form V 8xyz. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume: =
Transcribed Image Text:Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed
in the ellipsoid
+ +
9 36 25
G
=
1
Hint: By symmetry, you can restrict your attention to the first octant (where x, y, z ≥ 0), and
assume your volume has the form V 8xyz. Then arguing by symmetry, you need only look for
points which achieve the maximum which lie in the first octant. Maximum volume:
Transcribed Image Text:Find the absolute maximum and minimum of the function f(x, y) = y√x – y² − x + 3y on the
domain 0 ≤ x ≤ 9,0 ≤ y ≤ 1.
Absolute minimum value:
Absolute maximum value:
attained at
attained at
In each case, your second answer should be one or more points (x, y). If there is more than one
point at which the maximum or minimum value is attained, enter them all separated by commas
(e.g. (1,2),(1,3)).
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