When does the minimum value of p occur based on the relationship of q?

The minimum value of p occurs when q is at its minimum, as a general principle in various mathematical relationships. This is often observed in contexts where p is a function of q, such as linear, quadratic, or other functional relationships.

In many scenarios, when q takes on lower values, it can lead to lower outputs for p according to the defined relationship between the two variables. This reflects the nature of functions and how they respond to the input values they receive. Thus, when q is minimized, p is also pushed toward its minimum value.

This logical connection is grounded in the principle that if a function decreases as its input decreases, then at the minimum input level, the function is minimized as well. In contrast, the other options suggest relationships that either imply an increase in p or do not provide relevant information regarding the behavior of p in relation to q.