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.