Poll of the Day > What's the math term for a, like, parabolla that curves in opposite directions?

(+) Yeah! (+)

It's like a normal curved slope, but with a plateau in the middle

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It's still a parabola, just with the p of the equation being negative instead of positive.

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Cubic Equation

Do you mean a hyperbola?



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I mean like this (only neater 'cuz handdrawn)

https://imgur.com/5MBUEUq


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Lokarin posted...

I mean like this (only neater 'cuz handdrawn)

https://imgur.com/5MBUEUq

TheWorstPoster posted...

Cubic Equation

What's the middle between utopia and dystopia... is it just topia?

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Lokarin posted...

What's the middle between utopia and dystopia... is it just topia?

Reality

TheWorstPoster posted...

Reality

I mean more neutral using topia as a root

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Thats a smokabolla

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Lokarin posted...

I mean more neutral using topia as a root

Nope

https://www.symbolab.com/solver/step-by-step/%5Csqrt%7BTopia%7D

Lokarin posted...

https://imgur.com/5MBUEUq

If I had to take a shot at it, I'd say that this is a one-to-one, invertible, but not continuously differentiable function.

1. It's one-to-one because the function seems to be monotone-increasing.
2. It's invertible because it is one-to-one. It might not be invertible, depending on if the graph is flat on just one point or over some interval. If the latter, it is not invertible. If you do wish to define an inverse, you will want to restrict the domain of the original function to include just the bits of the function that are strictly monotone. You could include at most one point belonging to the plateau if you wish.
3. If the graph is flat on one point, then it is NOT continuously differentiable; the derivative at the plateau of the function is presumably zero, so the derivative of the inverse cannot be defined here.
3x. On the other hand, if the graph is never flat, then the function is continuously differentiable. Alternatively, if you restrict the domain so that all points of the plateau are excluded, then it would be continuously differentiable.

I would not say it looks like a cubic equation because of the function's behavior between zero and the plateau. It does not seem to be a graph of a polynomial of any odd degree, as a matter of fact. The tangent line does not seem to to be decreasing on the interval between zero and the plateau. I think this might answer your question.
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Lokarin posted...

I mean more neutral using topia as a root

the word "neutopia" is commonly used, though it doesn't seem to be an 'official' english word. there's a TG-16 zelda clone named neutopia, which also had a sequel. there's also an episode of Futurama titled Neutopia, in which everyone has their gender neutralized, and then later swapped.

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secxy



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