Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid 4x

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Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid 4x

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Find The Volume Of The Largest Rectangular Box With Edges Parallel To The Axes That Can Be Inscribed In The Ellipsoid 4x 1
Find The Volume Of The Largest Rectangular Box With Edges Parallel To The Axes That Can Be Inscribed In The Ellipsoid 4x 1 (96.75 KiB) Viewed 31 times
Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid 4x2​+1y2​+25z2​=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:
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