Back to basics with the drag curves.
First, the curves are for steady level flight where thrust equals drag. Second, it is normal to start with curves for EAS v. drag and EAS v. power required because it is EAS that determines drag. A shift to TAS is ok, but you then have to stretch the V axis to take account of the EAS/TAS ratio, which varies with density and therefore height and temperature. Keep it simple and use EAS. (Or IAS, since both are almost exactly the same at low altitude and at the speeds we are dealing with). Note that the type of propulsion is not relevant, these are aircraft drag curves
The two starting curves are EAS v. Profile drag and EAS v. Induced drag. Total drag is the sum of these two curves. Profile drag is Cdp times Vsq, Induced drag is Cdi times 1/Vsq so Total drag is CdpVsq + Cdi/Vsq. The values we choose for Cdp and Cdi will affect the shape of the curves and the numerical values we get for Vmd etc, but the curves remain straightforward examples of exponential curves of the form y = xsq, y = 1/xsq and y = xsq + 1/xsq. If you solve the Total drag curve for (A) the point where Total drag over V is a mimimum, which is where the tangent from the origin touches, and for (B) the point where total drag is at a minimum you will find that A is 1.316 times B.
Note that you don't know the actual speeds. These will depend on what values you use for Cdp and Cdi. Note also that we have assumed both Cdp and Cdi are constants. Because this and other hidden assumptions are not always true for the real world it is best to say "about 1.32"
Because in a jet, roughly, fuel flow is related to thrust, if you power this aircraft with a jet you will stay up longer at Vmd and fly furthest at 1.32Vmd. If you use a piston/prop engine, where fuel flow is related to EHP, engine horsepower delivered, you fly at Vmp for endurance and Vmd for range. If you look at the maths, you will se that flying at Vmd gives the best ratio of V over V x Drag, which is V over Power required. Also of interest is that on the graph of power required against V the tangent to the curve touches at minimum drag speed
All of this is for low level where you will have massively more thrust or power available that you actually need to fly for range or endurance. The next two stages are to get to a height here your engine can operate at max efficiency and the TAS/EAS ratio kicks in to extend your range - but that is another story
Dick