Hello everyone, while I was at a leadership conference my mind wandered and I found myself pondering the optimization of functions of the form
So I basically treated it as a function of one variable, and proceeding as such I arrived at a question.
Now by Leibniz's rule the above equation is equivalent to
Now I next looked for critical points.
If we let
Then the critical points occur at four points, namely :
Where is undefined
Less obviously, where . This obviously arises from the fact that
And also where is undefined.
Now here is where I ran into an anomaly, I found multiple cases where , satisfies two conatradicting critical point criteria, namely.
is undefined, but .
So this implies that this is a multi-valued function, so what does one do from here? Does one just sweep this doubly critical point under the carpet and continue? I hope not.
Any guidance would be appreciated.