Let's have a look at the simple example from documentation of findpeaks:
data=[25 8 15 5 6 10 10 3 1 20 7];
findpeaks(data)
When you see the marked points on the plot, none of them are differentiable since there are more than one tangent line that can be drawn at those points. Therefore:
That the derivative must be a zero at that point? Is this also satisfied?
No, it is not, as you can see.
