Tick function is a special function form, and its form is f (x) = ax+b/x (ab > 0), for the derivation of the lowest point of the hook function, we can follow the following steps:

1. First, we need to find the derivative of the function. The derivative of the hook function is f' (x) = a-b/(x 2). Then, we make the derivative equal to 0, that is, f'(x)=0, so we get x 2 = b/a. Because of a>0 and b>0, x>0. So we get the lowest abscissa x=√(b/a) of the hook function.

2. Next, in order to find the ordinate of the lowest point, we directly substitute x=√(b/a) into the original function f(x). You can get y=a×√(b/a)+b/√(b/a) after substitution.

3. Therefore, the lowest coordinate of the cross-check function is (√(b/a), a×√(b/a)+b/√(b/a)). Please note that this is only a derivation method, and there may be other methods to derive the lowest point formula of hook function. At the same time, for specific mathematical problems, it is necessary to make appropriate changes and adjustments in combination with the requirements and conditions of the topic.