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I have to find the point (x0,y0,z0) of the ellipsoid x^2/4 + y^2/9 + z^2/16 = 1 that minimizes de volume of the pyramid made by the planes z = 0, y = 0, x = 0, x>0, y> 0 , z>0 and the tangent plane to the ellipsoid at (x0, y0, z0). Can anyone help me please?
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