Question: Consider the following function: z = (x 1 + x 2 ) 2 + x 3 2 + 2x 1 x 3 + 2x 2

Consider the following function: z = (x1 + x2)2 + x32 + 2x1x3 + 2x2x3 .

a. Find the critical points of this function.

b. Does this function reach a maximum or minimum? Base on your answer on a discussion of the properties of the Hessian matrix of the function.

c. Find the equation of the tangent plane at the critical points identified by the FOC.

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