See the following chess case and it’s White's turn to move. If both White and Black play optimally, what is the minimum number of moves for White to checkmate the Black king?

The function f(x) is differentiable, continuous, and f(x) ≠ 0 for all values of x in the interval [4, 8]. Calculate f(6) given that f(4) = 1/4, f(8) = 1/2,