If your curve is based on a static formula, then just plug that into Wolfram|Alpha, find the one labelled as "Derivative" and that should give you a formula, which determines the slope of the curve at x. Plug the x position of the player in the curve's coordinate system and you get the slope. A value of 5 for instance means it goes up 5 units if you go 1 unit on the x axis.
If you can't do that, because it's procedural, then fake it. Pick a very small value (>0.001 will do it) and get the height of the curve at the player's position, then add this small value to the x coordinate and get the height there too. Subtract the former from the latter and divide by the small value. This is a good estimate (derivation is basically this but with a distance of 0). This won't really work if you predefine the heights, since that wouldn't leave you with enough precision.