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/sci/ - Science & Math

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7663344 No.7663344 [Reply] [Original]

Hey /sci/ does anyone know a way to find the vertex of an n-dimensional paraboloid?

I think it exists but I cannot find it.

Thanks /sci/

>> No.7663371

>>7663344
Help me sci you are my only hope.

>> No.7663374

What is your argument for the existence of that vertex ?

>> No.7663392

>>7663374
>I haven't taken calc III yet

>> No.7663403

>>7663344
take derivative and set to 0

>> No.7663431

Can you post an image of a 4D paraboloid's projection to 3D?

>> No.7663445

>vertex
is that what kids call critical points/stationary points nowadays?

>> No.7663535

>>7663445
Yes and I don't think you just set derivative to zero I remember there being some other way.

>> No.7663542

>>7663431
I can't find one.

>> No.7663642

>>7663535
You're talking about completing the square. Impossible to find a general solution for n>4, because this is equivalent to deriving a quadratic/cubic/etc. formula.

>> No.7663660

Wait, under which form is the paraboloid given to you?

>> No.7663667

>>7663660
I am looking for the general solution

>> No.7665270

>>7663344
its [math]t^{r^{i^{v^{i^{a^{l}}}}}}[/math]

>> No.7665273
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7665273

>>7665270
oh for christ sakes