Question: Using Lagrange multipliers, find the min and max distance from the point P(0, 1, 0) to the ellipsoid 2x + y + z =

Using Lagrange multipliers, find the min and max distance from the point

Using Lagrange multipliers, find the min and max distance from the point P(0, 1, 0) to the ellipsoid 2x + y + z = 6, and also find where the min/max distance is attained on the ellipsoid. You can assume that the absolute extrema must exist and be attained only at the candidate points determined by Lagrange multipliers.

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