How to find max and min X and Y?

Hi, I'd like to evaluate a closed curve to find the four points with max and min X and Y values. These curves are regular enough that creating a bounding box and finding the intersections produces the desired points. I'm guessing though that there is a way to evaluate the curve using some of the Analysis components that would give the answer directly, but I'm not familiar with how to use these.  Any help would be appreciated.

Thanks,

Eric