At first, I thought it was as simple as taking both functions adding them together then dividing by two, but this is not the case for what I am looking for. Here is a plot of the following:
y = x y = x^2 y = 1/2*(x^2+x) points exactly in between y = x and y = x^2
As you can see the red line representing y = 1/2*(x^2+x) does not land on the green points which are exactly in between the two functions y = x and y = x^2. What I am trying to learn how to do is figure out how to find the function which represents the exact middle between the two equations y = x and y = x^2.
I have already tried using an excel sheet to fit a line to all the green points I have calculated and still can't come up with a good line that fits.
I have looked into calculating the midpoint between two given points and that only helped calculate the points between the two equations, and didn't help towards obtaining a function that perfectly represents the line between y = x and y = x^2.
Thanks for any help or suggestions towards the right domain of math reserved for solving cases like this one.