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Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.

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Newton's minimizing method converge to local maximum [closed]

I have to minimize $f(x)=x^4-24x^2$ starting on the point $x_o=1$. The method converge to $x=0$, but i know that the solution is $x=+-2\sqrt{3}$. The hessian and the derivate of the function are $C_2$ …