I simply want the solution as Desmos solves it automatically

I don’t want to expand the crazy polynomial it will make as it literally solves it but I don’t want the graph I want both of the x’s

You can do it using regression to ‘solve’ the equations if you want. For instance:

- I’ve turned the function you want =1 into a function of p (use any letter)
- I’ve asked it to find two variables, [q and w] (use any variables) such that the function ~1 at those points
- I’ve forced q to be bigger than w with the condition at the end
- I’ve added a bit to w otherwise it can yield the same value due to rounding/variance

Then your two solutions are x=q and x=w.

Let me know if none of this makes sense.

Thanks alot, i could definitely use this for other projects in mine but I found another way to simply have some constant line of 1 be tangent whatever function i put in.

Thats pretty much it thank you however

Can you share your method so that others can see how you resolved it?

here

I used trigonometry since working with angles is far easier with that polynomial I would have to solve

sorry for taking 2 days

I adapted your solution. Throughout you can use f(x_1) instead of h(x_1), and more explicitly define where you used h(0). I also used a parametric line segment instead of needing to calculate L_1 and L_2 to keep your segment a consistent length. Desmos | Graphing Calculator

h(0) is just for the angle calculation it doesn’t really matter, but yeah a parametric equation was always on my mind but I was looking for a way using the “limit” {} of the function that is the slope of the function at that approximate point.