There is a way to find local minima outside of a BASIC program using the CALC menu on the graphscreen, but no function specifically for programs. Here's one way I did it (based on your idea of pulling a table from the calculator). This will display the X,Y for the local minimum given a Left and Right bound:
Repeat I≤10^-3 <-- Tweak this to determine the accuracy of the answer (smaller exponent = more accurate = slower computation)
You can also edit this code to find local maxima by replacing all SortA( commands with SortD( commands. I didn't include it here, but you should also clean-up lists 1-4 if you're intending for others to use it. Hope this helps!