# Determining the intersection of two functions with errors on parameters

Let's assume I want to calculate the intersection points of two functions $f(x)$ and $g(x)$. That is simple enough, I define my functions, e.g. like so and use Solve

a = 5.5
b = 7.0
c = 0.2
f[x_] := a*x + 2;
g[x_] := b*x^2 + c*x;
Solve[{f[x] == g[x]}, {x}, Reals]


But what if I had errors on my parameters? Of course, first I use the "non-erronous" parameters (5.5, 7.0, 0.2) to calculate the intersection, but how can Mathematica calculate the error on this result with Gaussian error propagation? For context, this is for analysing lab data that were fitted with two linear functions whose intersection I need to calculate, and it gets tiresome for lots of data.

I haven't really used Mathematica yet for error analysis, so I'm a bit stumped on where to look.

• Try a = 11/2 + Interval[{-1/6, 1/6}]; b = 7 + Interval[{-1/8, 1/8}]; c = 1/5 + Interval[{-1/25, 1/25}]; f[x_] := a x + 2; g[x_] := b x^2 + c x; Solve[{ f[x] == g[x]}, {x}, Reals] Jan 23 '18 at 13:15
• Very helpful already, thank you! I now use two non-erronous functions to give me the solution and use two other functions $h(x)$ and $j(x)$ that add variables aerr,berr,cerr to a,b,c consisting of the Interval to obtain the upper and lower limits of the error (with two separate Solve[...]. Does that seem correct? Jan 23 '18 at 13:31
• That does under assumption that you are aware what lies beneath. Jan 23 '18 at 13:55