Is the reference point (x, y) above or below the non-linear equation? BACKGROUND
In short, I have a series of 3 to 10 data points that will be used to represent a curve.  For example: 


*

*$X=0, Y=10$

*$X=4, Y=7$

*$X=9, Y=12$

*$X=16, Y=10$


What I am trying to do is determine whether or not a reference point is above or below the curve. 
My gut feeling is that for people in the know, this is a relatively straight forward problem to solve.  Unfortunately, my area of expertise is programming... not mathematics :(
Any guidance you can provide would be greatly appreciated.
ADDITIONAL NOTES
If it helps, I have access to the Math.NET library.

From what I understand you want to create a curve that passes through the points {(0,0),(4,7),(9,12),(16,10)}. This is called interpolation. This website might help in implementing it using math.net: https://numerics.mathdotnet.com/
Information from the graph you arrive at using interpolation is not reliable beyond the points you did the interpolation with.
