We know that acceleration = dv/dt. If an object is thrown upward, v=0 at the highest point. Hence acceleration (from above relation) must be 0,...

Hello!

Luckily, there is no contradiction. You are right that that at the highest point and that the acceleration due to gravity is constant.

The only incorrect statement you use is that if It is not true in general.

Recall the definition of a derivative or which are the same. For a function :

...

Hello!

Luckily, there is no contradiction. You are right that that at the highest point and that the acceleration due to gravity is constant.

The only incorrect statement you use is that if It is not true in general.

Recall the definition of a derivative or which are the same. For a function :

If for some specific moment becomes:

But it doesn't have to be zero! For example, in our case is a linear function. For any even for where

so the limit is also (this means downwards).

There is a grain of truth in your assumption, nevertheless. If at some entire interval around a point then  for all small enough, and