The plane z + y + z = 1 and the cylinder z + y? = 1 intersect in a curve, as shown by the 3D model below. To find the largest value that the function f(z,y, z) = 2z + 4y + z can have on this curve, use Lagrange multipliers to maximize f subject to the constraints z + y + z = 1 and z² + y² = 1. Maximum value: 2.

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A: Method of Lagrange's MultipliersWe have Assume

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