Questions regarding properties

1. Sep 8, 2014

MathewsMD

If there is a graph that has a discontinuity (e.g. at x = 3) and then the there is a point much lower than the limit at 3, is that point at 3 considered a local minimum? Also, if the graph starts w/ a discontinuity at its "highest point", does it have an absolute maximum?

2. Sep 9, 2014

haruspex

I'm guessing you mean, in the first question, that the function would have been continuous at x if f(x) had been some value y, but the discontinuity is that it has a lower value than y. If so, yes, I would say that constitutes a local minimum.
For the second question, I guess you mean, again, that the discontinuity consists of the function taking a lower value than the approach limit, and nowhere takes a value as high as the approach limit. If so, there is no absolute maximum.