I don't understand why you would use memoization for fibonacci ever and hence its relevance for dynamic programming. It can be solved with a tail recursive function with three input parameters. Solution left to the reader as an exercise.
But how to you systematically deduce the tail recursion version?
I feel like, in this case, the recursivity in definition of Fibonacci and the recursivity in the tail recursion is just a coincidence, with the second just being a contrived way to write the loop you get after applying dynamic programming and trimming the table to only the last two elements.
I don't understand why you would use tail recursive functions for fibonacci ever and hence its relevance for dynamic programming. It can be solved with a simple equation with one input parameter. Solution left to OP as an exercise.
