Accuracy of numsolve in TI, CASIO

[lrdheat]

I notice on my TI-30X Pro MathPrint...if I solve d/dx to =0 for (x^2 +7x +3)/ ^2, the solution found is most accurate when choosing an epsilon of 1E-05. Why is this the optimum choice? On my CASIO fx-991EX, the solution is more accurate, last digit shown is correctly rounded...wonder what epsilon is used, and what is different in it’s solve methodology...