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Math geeks! I have a question. I have a 3rd degree polynomial. I want to tweak the function so that the open-downward parabola of the curve gets more narrow (see rough sketch), without changing the max at 0 and the min at 1. Can i do that? How? https://www.desmos.com/calculator/qjpqor6qak

@daniel_bohrer Oh that would be okay, i am only interested in the domain (0, 1)

0 = a*1^3 + b*1^2 + c*1 + d,

1 = a*0^3 + b*0^2 + c*0 + d.

Additionally you have the constraints of the first derivative (i.e. the slope) = 0 in those points. (sorry, I don't remember the formula right now :D) but setting t' to those points = 0 gives you four equations in total, and you can then use Gauss-Jordan elimination to solve for a, b, c and d.

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me: how do you derive a third-grade polynomial again?

f(x) = 2t^3 - 3t^2 + 1

f'(x) = 6t^2 - 6t

Integral: 0.5t^4 - t^3 + t

@daniel_bohrer Thanks Daniel, i'll give that a shot!

@cevado Ya i'm gonna try out some things. Thanks!

@claus (t-1)^2 * (t+0.25).

But it will still look very different from green. Cubic can't approximate that well.

@waxwing I want to preserve both the touch one at t=0 and touch zero at t=1 points ;)

@claus doh, i didnt read your first post.

Can multiply original suggestion by 4 for that.

Daniel Bohrer@daniel_bohrer@chaos.social@claus mathematical answer: it is possible, but it will also change the slow of the upwards-facing part right of x=1.