Exercise 4. For the function f(x) = x² + 2x2 + 4x₂ + 4x2 prove by induction that the method of steepest descent applied with an initial guess x¹) =0 generates the sequence {x(*)} where 2 x(k+1) = -2, 3k 3 Hence deduce the minimizer of f(x). Note: - {x(k+1}x=(-2,-1)" vf(x) = (4 (-1) + 4) (2(-2) 3)+4)=() 0²/(x) = (²9) > 0.

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