Exercise 4. For the function f(x) = x² + 2x² + 4x₁ + 4x2 prove by induction that the method of steepest descent applied with an initial guess x¹) =0 generates the sequence [*(*)} where 2 x(k+1) = 2, (3)-¹) 3k Hence deduce the minimizer of f(x). Note: {x(k+1}x=(-2,-1)" (2(-2) vf(x) = (4(-1) + 4) +4)=(0) + v2f(x) = (ỏ 4) >o 1

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