Is the maximum lift-drag ratio found at minimum drag?
Well, for all L/D curves and D curves, the assumption is that the weight of the aircraft is constant and that there is no acceleration. Therefore the lift equals the weight (neglecting the small vertical component of thrust). So lift is a constant in these curves. 

The rest is simple mathematics; the maximum of $\frac{1}{f(x)}$ occurs at the minimum of $f(x)$ (when $f(x) &gt; 0$), so the maximum of $\frac{L}{D}$ coincides with the minimum of $D$.