I'd like some help in clarifying what constitutes an explanation and what is needed to justify a function increasing at an increasing rate given a table of values (like #3 on the AB Practice exam)
Do you have to find all of the secant slopes to justify increasing at an increasing rate? My thinking is that you do. Otherwise it could decrease on an interval and then would not be increasing on the entire interval.
If a student discusses that the secant slopes increase at an increasing rate but never shows the values of these secant slopes, is that enough for an "explanation" point or do you really have to have the data to back up an explanation?
Can a conclusion be based on words only and no mathematics behind the words? Again, my thinking is that in this case, no, words are not enough.
Any help with these questions will be appreciated.