Hi

I knew I should have kept awake during these classes, but sleeping was important back then

What I want to know is at what point x a power function (x^n) is tangent to a 45° line.

So if I have i.e:

f(x) = x^2.6 (or any number),

at what point x does it “climb” at a 45° angle?

Sounds like what I’m looking for is when is the derivative = 1, right? Derivative would be (2.6*x)^(2.6-1), so I plug it into a solver and get this result, which in turns tells me I need to “rationalize decimal numbers”, whatever that means

I found some code examples based on various languages, but I’m not much of a programmer. I see the basic versions seem to use loops, which doesn’t bide well for a Cycles approach.

The idea is to convert a linear input (known to be 1:1, or 45°) to something that is linear for a given range (x), and then switch to a power function with power n. I.e. no values change from 0-3.7 (or whatever), but from 3.7 onwards it looks like a power function that starts with an angle of 45° (but can be any power I choose).

Does anyone have an idea how to attack this?

Alternatively I could solve for a given number of useful presets of n and hardcode the output by a given n.

Edit: Oh my god, never mind. Apparently 1/n is exactly what I’m looking for (except in number format that makes sense), but feel free to correct me if I’m wrong.