I am trying to do a non-linear programming work. We have two functions: $\displaystyle f(x)=x^2/2+e^{-x} $ and $\displaystyle g(x) = x^4-32x^2$. I just want to know how exactly one can get the minimum of x, x*. For example using the newton method:

Code:

k ak F'(x) F''(X) k ak g'(x) g''(x)
1 2,0000 1,8647 1,1353 1 0,2000 -12,7680 -63,5200
2 0,3576 -0,3417 1,6993 2 -0,0010 0,0645 -64,0000
3 0,5587 -0,0132 1,5719 3 0,0000 0,0000 -64,0000
4 0,5671 0,0000 1,5672
5 0,5671 0,0000 1,5671

So I caluclate and get this but then how can I determine the minimum of x, x*?