Use Lagrange multipliers to find the maximum area S of a rectangle inscribed in the ellipse...

  

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Use Lagrange multipliers to find the maximum area S of a rectangle inscribed in the ellipse x² + 16 49 = (-x, y) II S = 1 (x, y) (x, -y) (Give your answer as a whole or exact number.) Use Lagrange multipliers to find the maximum area S of a rectangle inscribed in the ellipse x² + 16 49 = (-x, y) II S = 1 (x, y) (x, -y) (Give your answer as a whole or exact number.)