Let F'(x)=0, which is wrong. I don't know if you are wrong or wrong, because the derivative of the reciprocal of the fraction is meaningless, and x approaches infinity at this time. Actually, what I want to ask you is: Is it f(x)= 1/x or F(x)= 1/x?

Is F(x) a constructor? If there is, you can write the expression, otherwise others can't understand it, and I can't understand it either. Only in this way can I know why F(-2b/3a)=0.

F'(x)=0 is not an extreme value, but the slope (derivative) of the change point (x). But from here I can confirm that f(x) should be the constructor of both F(x) and g(x).