What about the power curve? Aren't the drag curve and power curve two different things?
AFAIK, no. The "power curve" has actually not so much to do with power but plots drag against airspeed. Normally, more speed means more drag (as with cycling against a headwind, for example). For airplanes, however, there are two kinds of relevant drag, parasitic and induced, the former one representing the "cyclist's" drag and rising with speed, the other one rising with the amount of lift produced.
As the airplane slows down, parasitic drag decreases but induced drag increases. At a certain point (which corresponds to glide speed for maximum range IIRC), slowing down even more would increase total drag, so if you get slower than that you would have to increase power just to maintain airspeed (I haven't heard of or read about slowing the plane down by adding power, though), as also explained in the previous post.
This thread from another forum may be your friend, as may Google, if you are still confused
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