As we will see in Chapter 4, when looking for maxima and minima of a differentiable function F: X ⊆ Rn → R, we need to find the points where DF(x1, . . . , xn) = [0 · · · 0], called critical points of F. Let F(x, y) = 4 sin (xy) + x3 + y3. Use Newton’s method to approximate the critical point that lies near (x, y) = (−1, −1).
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