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Empty
 one year ago
5x^2+y^4 = 9
Evaluate y'' at x=2, y=1

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

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dan815
 one year ago
Best ResponseYou've already chosen the best response.0it depends do u want it to mean anything

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0he wants acceleration at that point (2,1) I guess.

pujan20
 one year ago
Best ResponseYou've already chosen the best response.0@dan815 i agree with fbi2015

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.0wait a sec i got the answer :)

Empty
 one year ago
Best ResponseYou've already chosen the best response.0There is an "answer" no problem. But that's not what I care about.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0true that, you can swabb answer from wolfram all day everyday

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0@dan815 yeah it mean something in complex maybe xD

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.0u 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
 one year ago
Best ResponseYou've already chosen the best response.0Stop solving it, I don't care, I only care about this: x=2, y=1 \[5x^2+y^4=9\] \[5*4+1 \ne 9\]

Empty
 one year ago
Best ResponseYou've already chosen the best response.0\[y'' = 12.5\] I believe, just so no one else tries to solve it haha

dan815
 one year ago
Best ResponseYou've already chosen the best response.0like what does it mean to have complex routes

Empty
 one year ago
Best ResponseYou've already chosen the best response.0I 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
 one year ago
Best ResponseYou've already chosen the best response.0like 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
 one year ago
Best ResponseYou've already chosen the best response.0maybe something similiar to that is happening here

dan815
 one year ago
Best ResponseYou've already chosen the best response.0the 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
 one year ago
Best ResponseYou've already chosen the best response.0the way the 2nd derivate behaves in this case*

dan815
 one year ago
Best ResponseYou've already chosen the best response.0the point (2,1) could belong to some other function too, a function along which the 2nd derivative is constant

dan815
 one year ago
Best ResponseYou've already chosen the best response.0you can try to think of a function where the 2nd derivative will be cosntant along some other curves

Empty
 one year ago
Best ResponseYou've already chosen the best response.0Ok 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
 one year ago
Best ResponseYou've already chosen the best response.0what would the gradient and the gradient field of this function look like for example could be an example

dan815
 one year ago
Best ResponseYou've already chosen the best response.0but 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
 one year ago
Best ResponseYou've already chosen the best response.0what would the gradient and the gradient of the gradient* field of this function look like for example could be an example

dan815
 one year ago
Best ResponseYou've already chosen the best response.0im not really satisfied with that lol but ya

dan815
 one year ago
Best ResponseYou've already chosen the best response.0also i was thinking about that complex root stuff with a parabola

Empty
 one year ago
Best ResponseYou've already chosen the best response.0Hmmm I don't really understand what you mean

dan815
 one year ago
Best ResponseYou've already chosen the best response.0its gonna give us a complex answer in uv plane but what does that complex value mean in x,y plane

dan815
 one year ago
Best ResponseYou've already chosen the best response.0like suppose you have a transformation of coordinates and you tried to solve for the complex roots

dan815
 one year ago
Best ResponseYou've already chosen the best response.0like 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
 one year ago
Best ResponseYou've already chosen the best response.0so technically for example your function 5x^2+y^2=9 we werent able to thjink about this as having complex routes

dan815
 one year ago
Best ResponseYou've already chosen the best response.0but for some transformation of coordinates u can think about complex roots

Empty
 one year ago
Best ResponseYou've already chosen the best response.0Well 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
 one year ago
Best ResponseYou've already chosen the best response.0ya i was thinking about that lol, but who says complex root arent just nonsense too

Empty
 one year ago
Best ResponseYou've already chosen the best response.0Me, I say that they aren't

dan815
 one year ago
Best ResponseYou've already chosen the best response.0it has a use so they arent nonsense all of a sudden

dan815
 one year ago
Best ResponseYou've already chosen the best response.0what if these will have uses later then

Empty
 one year ago
Best ResponseYou've already chosen the best response.0complex 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
 one year ago
Best ResponseYou've already chosen the best response.0okay himm hoow about this argument

dan815
 one year ago
Best ResponseYou've already chosen the best response.0is it possible that some non parabolic functions can be defined in sum of an infinite set of parabolic functions

dan815
 one year ago
Best ResponseYou've already chosen the best response.0okay well the way i see it is that

dan815
 one year ago
Best ResponseYou've already chosen the best response.0this complex value came because someone wanted to see the intersection of a parabola with the y=0 line

dan815
 one year ago
Best ResponseYou've already chosen the best response.0but we can pick other lines for other functions

dan815
 one year ago
Best ResponseYou've already chosen the best response.0it 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
 one year ago
Best ResponseYou've already chosen the best response.0im just saying random stuff right now :>

Empty
 one year ago
Best ResponseYou've already chosen the best response.0hmmm so wait give an example cause I'm not seeing these parabolas or something like wanna start a twiddla or cosketch or whatever
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