I think what inman is talking about, is creating a line in the cartesian coordinate system, by using 2 adjacent data points. If the "slope" of the line is positive, then shift data points by one, so the "previously second" x value, is now the first, and compute the next slope. Where the slope turns from a positive to negative value, is a "local" peak.

The slope of a line is y = Mx + b, where M is the slope. M is usually (y2 -y1)/(x2 - x1).

I think Pustular Postulant's method is probably faster.