I am trying to do a non-linear programming work. We have two functions: and . I just want to know how exactly one can get the minimum of x, x*. For example using the newton method:
So I caluclate and get this but then how can I determine the minimum of x, x*?
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
Well the minimum for the function f(x) will be where f'(x)= 0 and f''(x*)>0.
Same goes for g(x)
OK I understand f'(x) but what did you mean by f"(x*) or you meant f"(x)? Because I am looking for the minimum, x*, so how can I find f"(x*) when I don't even have x*? If you mean the minimum, x*, is where f'(x) = 0 and f"(x)>0, then yeah I understand. So that would be x* = 0.5671 for f(x) but then I don't know how I can get x* for g(x) because although we have a place where f'(x) = 0, we have no where where f"(x)>0?
Thanks in advance.
OK I read a some stuff on the internet and I found out that the minimum is where f'(x) = 0 and f''(x)>0. If f''(x)<0, then that is a maximum point but in the question we were asked to find out the minimum, not the maximum so I am confused. When f'(x) = 0, f"(x)<0 so I am wondering how I can find the min. for this equation.
x* is the solution to f'(x)=0.
Originally Posted by Keep
OK thanks. Substituting we get: for x* = 0, g(x*) = 0, for x* = +/-4, g(x)= -256. So out of those three values for x* which one is the minimum?