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:

```
Prompt L,R
.1(R-L→I
ClrList L₃,L₄
Repeat I≤10^-3 <-- Tweak this to determine the accuracy of the answer (smaller exponent = more accurate = slower computation)
ClrList L₁,L₂
For(X,L,R,I
X→L₁(1+dim(L₁
Y₁(X→L₂(1+dim(L₂
End
SortA(L₂,L₁
L₁(1→J
J→L₃(1+dim(L₃
L₂(1→L₄(1+dim(L₄
J-I→L
J+I→R
.1I→I
End
SortA(L₄,L₃
Disp L₃(1),L₄(1
```

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!