# Get the value of boundary point

I used the $$NMinimize$$ instruction to calculate, but what I got was the dt value of the red circle. If I want to obtain the dt value of the green circle, how do I obtain it? The code for generating the curve is as follows:

vc = Function[t,
23.999999999999996 +
55.082039324993595 E^(-267.92850868181444 t) -
79.08203932499359 E^(-186.61694586364015 t)];
condunequal = Abs[-1/2 dt (vc'[t + dt] - vc'[t])] <= 1/50000;
condequal = Abs[-1/2 dt (vc'[t + dt] - vc'[t])] == 1/50000;
RegionPlot[condunequal, {t, 0, 2/25}, {dt, 0, 0.0001},
FrameLabel -> {t, dt}]
maxvc = NMinimize[{dt , condequal, 0 <= t <= 2/25,
0 <= dt <= 0.0001}, {t, dt}, MaxIterations -> 1000]

• Remove MaxIterations option and your will get the desired point
– Acus
May 12 at 8:36
• @Acus I removed $MaxIterations$ and obtained a result of 5.64137*10^-9. However, from the graph, it can be seen that the value of the green circle is approximately 5.3*10^-6, and the difference is still significant. May 12 at 8:50
• It might be a precision issue, since you use very small numbers (10^(-117)) and do computation with machine arithmetic.
– Acus
May 12 at 9:13
• @Acus Sir, I tried using higher accuracy, but it didn't achieve the desired effect. May 12 at 11:09

We modified the condition.  10^-10 <= dt <= 0.0001.
sol = NMinimize[{dt, condequal, 0 <= t <= 2/25,
` 