EventLocator

Q: The solution to the differential equation with is .

Solving the same equation numerically, I tried using the event function to find the extrema of .

How can I find those points where ?

A: Mark Sofroniou (marks@wolfram.com) answers: An event is located when a change in sign in the event function is detected. For the function , the sign is practically always negative and the chance of hitting zero is infinitesimal.

You can construct an appropriate event function for extrema, where , by noting that . Then it is possible to use the Direction option to restrict the detection to points corresponding to a maximum.