How to find a local minimum around a point you click in a graph?

I have a lot of different graphs, where I want to find the minimal point of where the line is going up towards it's peak. I would like to do this by inserting a piece of code where I have to click somewhere in the graph (close to the point I want to find) and that it automatically selects and saves the local minimum. The same I would like to do for the maximum. How to do this and print this out in code?

Graph of what I mean (ignore the yellow dot, that should be more to the right).

[KSSV]

There are inbuilt commands..read about islocalmin, islocalmax.