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 + 2x₁ x₃+ 2x₂x₃ .

a. Find the critical points of this function.

b. Does this function reach a maximum or minimum value? (Check for Local 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 first order condition.

(Hint from my TA: if you prove that there are unlimited critical points, think about whether there is a need for you to prove anymore things in b. and c.)

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