The inflexion formula of hook function is plus or minus √b/a and plus or minus 2√aby. Hook function is a general hyperbolic function similar to inverse proportional function, and its form is f (x) = ax+b/x (ab >; 0). Named after the image, it is also called double hook function, hook function, stop function, Shuang Yan function and so on.

How to find the inflection point of hook function

Because the function image is similar to the Nike trademark, it is also called Nike function or Nike curve. Common a=b= 1. The image of hook function is two curves with y axis and y=ax as asymptotes respectively, and the product of the distance from any point on the image to the two asymptotes is exactly the product of the sine value of the included angle of the asymptotes (0- 180) and |b|.

The test function y = x+a/x (a/x>0), when x>0, a/x>0, x times a/x equals a. According to the basic inequality x+a/x≥2√a, the equality sign holds if and only if x = a/x =-√ a, that is, when x = √ a.