The diagram shows part of the curve \(y = \frac{8}{x} + 2x\) and three points \(A, B,\) and \(C\) on the curve with \(x\)-coordinates 1, 2, and 5 respectively.

A point \(P\) moves along the curve in such a way that its \(x\)-coordinate increases at a constant rate of 0.04 units per second. Find the rate at which the \(y\)-coordinate of \(P\) is changing as \(P\) passes through \(A\).