5x^2+y^4 = -9
Evaluate y'' at x=2, y=1
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This question seems to have an answer, but does the answer actually mean anything?

- Empty

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- dan815

it depends do u want it to mean anything

- anonymous

he wants acceleration at that point (2,1) I guess.

- pujan20

@dan815 i agree with fbi2015

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## More answers

- dan815

who says its d^2y/dt^2

- anonymous

well if x is time

- Empty

y'' = d^2y/dx^2 here

- imqwerty

wait a sec i got the answer :)

- Empty

There is an "answer" no problem. But that's not what I care about.

- anonymous

true that, you can swabb answer from wolfram all day everyday

- ikram002p

@dan815 yeah it mean something in complex maybe xD

- dan815

|dw:1440371299983:dw|

- imqwerty

u have to double differentiate the equation with respect to x nd then u'll get an equation in x nd y then u jst put the values nd get the answer LOL

- Empty

Stop solving it, I don't care, I only care about this:
x=2, y=1
\[5x^2+y^4=-9\]
\[5*4+1 \ne -9\]

- dan815

i see

- Empty

\[y'' = 12.5\] I believe, just so no one else tries to solve it haha

- dan815

maybe in complex plane

- dan815

like what does it mean to have complex routes

- dan815

roots*

- Empty

I don't think so, because although there are complex solutions to \(5x^2+y^4=-9\) x=2 and y=1 are still not solutinos

- dan815

like can we try a simpler example
Y=x^3
y'=3x^2
y''=12x
what does y''(0,2) mean?
0,2 is not a solution yo y=x^3 but at the same time it just works because 0 can be put in for x

- dan815

maybe something similiar to that is happening here

- Empty

Yeah that looks good

- dan815

the way the 2nd derivative behaves is just not a function of the y domain
so with other functions maybe u can get it to not be functions of some lines and the point 2,1 happens to be on that line

- dan815

the way the 2nd derivate behaves in this case*

- dan815

the point (2,1) could belong to some other function too, a function along which the 2nd derivative is constant

- dan815

you can try to think of a function where the 2nd derivative will be cosntant along some other curves

- dan815

|dw:1440372327851:dw|

- Empty

Ok I kinda see what you're saying, add a constant value to our original equation and we have a family of curves:
\[5x^2+y^4+C = -9\]
This will have all the same derivatives as the original case C=0 but now we can also find the curve that satisfies x=2 and y=1. I guess this would be a way to think of it?

- dan815

ya that makes sense

- dan815

what would the gradient and the gradient field of this function look like for example could be an example

- dan815

but i see what u mean this only works out if theres a constant and some variation so that this function exists everywhere over the space

- dan815

what would the gradient and the gradient of the gradient* field of this function look like for example could be an example

- dan815

im not really satisfied with that lol but ya

- dan815

also i was thinking about that complex root stuff with a parabola

- dan815

|dw:1440373563511:dw|

- dan815

|dw:1440373638686:dw|

- Empty

Hmmm I don't really understand what you mean

- dan815

its gonna give us a complex answer in uv plane but what does that complex value mean in x,y plane

- dan815

like suppose you have a transformation of coordinates
and you tried to solve for the complex roots

- dan815

like okay for example x^2+y^2=1
is not a well defined function with a simple x domain or y domian it has to have both x,y domain, its a 1:1 function in theta:r
so im saying if u take your given function and do some transformation of coordiantes where its 1:1
and then fiding complex roots in that domain what does that complex number mean in x,y domain?

- dan815

so technically for example your function 5x^2+y^2=-9 we werent able to thjink about this as having complex routes

- dan815

but for some transformation of coordinates u can think about complex roots

- dan815

i dunno =.=

- Empty

Well wait I think there's a difference here between complex answers and nonsense answers.
For example, a set of complex values that work for \(x^2+y^2=1\) would be x=2 and \(y=i \sqrt{3}\)
A set of nonsense values that don't work are x=2 and y=2.

- dan815

ya i was thinking about that lol, but who says complex root arent just nonsense too

- Empty

Me, I say that they aren't

- dan815

lol

- Empty

lol

- dan815

it has a use so they arent nonsense all of a sudden

- dan815

what if these will have uses later then

- Empty

complex answers are just expanding your domain and range, nonsense answers are just picking values that don't satisfy the equation.
So we can pick a pair of complex nonsense answers or a pair of real nonsense answers.

- dan815

okay himm hoow about this argument

- dan815

is it possible that some non parabolic functions can be defined in sum of an infinite set of parabolic functions

- dan815

okay well the way i see it is that

- dan815

this complex value came because someone wanted to see the intersection of a parabola with the y=0 line

- dan815

but we can pick other lines for other functions

- dan815

it will still give specific answers, for each line and which domain you pick, but yet every point can be covered depending on how u change your domain and what line you pick

- dan815

im just saying random stuff right now :>

- Empty

hmmm so wait give an example cause I'm not seeing these parabolas or something like wanna start a twiddla or cosketch or whatever

- Empty

http://cosketch.com/Rooms/hkedsyu

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