max picks the largest value from all past or current numeric values. min picks the smallest value from all past or current numeric values. For example, given the following case fragment:

Cholesterol     7.3    5.6    6.1
Triglyceride    1.1    0.8    pending
HDL             2.2           1.9

max Cholesterol is 7.3

min Triglyceride < 1

HDL at max Cholesterol is 2.2