Thank you all so much for your input.
Looking at the THRUST / DRAG curve (which are curves of force, not power). The speed for the use of least THRUST is the speed of MIN DRAG. To fly any faster or slower than V MIN DRAG you will have to use more thrust.
But thrust is fuel!
According to my books and what I have been taught V MIN DRAG is found on the power curve by drawing a straight line from the origin until it makes a tangent with the POWER REQUIRED curve.
This makes V MIN DRAG faster than V MIN POWER.
But we know from the THRUST/DRAG curves that to fly at any other speed than V MIN DRAG requires more THRUST.
How can more THRUST mean less POWER and therefore less fuel?