The correlation between the Federal Fund rate and the DXY. In fancy mathematical terms, let's assume to start with the function F(x)= USD, thereby we can assume that the DXY it's the first derivative of f(x)=USD, considering that the DXY has been built as the average index of all the other currencies exchange rate in proportion to the USD. So the first Derivative for f(X)= USD has been made with the DXY. In this instance, we could argue that the Federal Fund Rate becomes then the Second Derivative of F(X)=USD, with respect to DXY.
Studying the second derivative behaviour, we could argue that in mathematical terms the 0% Federal Fund rate derives the Local Minimum for the d''f/dX^2 , in fact hiking interest rates starts to make the Federal Fund rate curve convex, otherwise Concave to the upside, thereby in graphic terms we can see that the 0% Federal Fund Rate= Local Minimum thereby the D''f/dX^2 starts to become positive from there. This can be reflected in the First derivative DXY, which shaped a Convex curve going to the upside that will tend to the Local Maximum, which could be DXY=122. So the function f(X)=USD would be increasing, which means a stronger U$Dollar.
Studying the second derivative behaviour, we could argue that in mathematical terms the 0% Federal Fund rate derives the Local Minimum for the d''f/dX^2 , in fact hiking interest rates starts to make the Federal Fund rate curve convex, otherwise Concave to the upside, thereby in graphic terms we can see that the 0% Federal Fund Rate= Local Minimum thereby the D''f/dX^2 starts to become positive from there. This can be reflected in the First derivative DXY, which shaped a Convex curve going to the upside that will tend to the Local Maximum, which could be DXY=122. So the function f(X)=USD would be increasing, which means a stronger U$Dollar.