/sci/ - Science & Math

While making an erotic text game I came across this problem:

I have some variable [math]F[/math] which changes as a function of [math]w[/math].
For any given starting value [math]w_0[/math] and a change in [math]w[/math] of [math]\Delta w[/math], the relationship is thus:
[eqn]F(w_0+\Delta w)=\dfrac{w_0f(w_0)+D\Delta w}{w_0+\Delta w}[/eqn]
Where:
[math]D[/math] is a parameter [math]0\leq D\leq 1[/math] that changes according the player's actions in the game.
[math]f(w_0)[/math] is some other function. Right now it is defined as [math]f(w_0)=\dfrac{w_0}{71.6h^2}[/math] ([math]h[/math] is some constant), but it could change in the future to [math]f(w_0)=\dfrac{w_0}{64.1h^2}-0.176[/math].
So to put it another way:
[eqn]F(w_0+\Delta w)=\dfrac{\dfrac{w_0^2}{71.6h^2}+D\Delta w}{w_0+\Delta w}[/eqn]

Is there a way to make this into a nice little [math]F(w)[/math] expression?
I COULD just program the entire thing as-is directly into the game code, but I need to determine the exact values of [math]D[/math] to plug in there. I don't want to manually test out values between [math]0[/math] and [math]1[/math].


Is such a function even possible..?
Someone please help me out, I've never been good at calculus