[itchyjunk]

No, I see your point. And its valid. But I was getting at something slightly different. I don't think the "tsunami" prophecy will come to be true over night. Speaking in terms of average rate of change would be over valuable rather than instantaneous rate of change. Ofcourse, the average might equal the instantaneous at some point if mean value theorem hold true, but just talking in terms of instant change makes it sound all doom and gloom when it's really not.

Even the Earth might not go out of orbit instantaneously if the Sun were to suddenly disappear.