Question: Consider the following unconstrained minimization problem: minimize: f(x) = 5x 4 1 +6x 2 4 6x 2 1 +2x 1 x 2 +5x 2 +15x

Consider the following unconstrained minimization problem: minimize:

f(x) = 5x⁴₁ +6x₂⁴ 6x²₁ +2x₁x₂ +5x₂ +15x₁ 7x₂ +13 (1)

(a) Write out the FONCs for this optimization problem.

(b) Using the initial guess [1, 1]T , apply Newtons method for at least 6 iterations to obtain an approximation solution to the optimization problem above. Make sure that you have found a minimum and not a maximum.

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