ALEX,
The problem is not in the calculus, but is in the conclusion that you are drawing from it.
Mathematics can be a very powerful tool, but we must be very careful in how we use it. Whenever we try to apply it to real world situations we inevitably impose a number of simplifications. These can have a marked effect on the accuracy of the results we produce.
Your assumption that total drag is proportional to V squared plus 1/V squared is based in part on the assumption that CDP is constant. This is not actually true but is simply a reasonable approximation unless we want really accurate results. Because of this fact, total drag is not exactly proportional to V squared plus 1/V squared. If making accurate predictions of aerodynamic effects were simply a matter of doing a few sums then there would be far fewer wind tunnels in the world!
You are trying to prove one hypthesis by basing your argument on another hypthesis. Unless you are prepared to prove each one in turn then you will prove nothing.