## 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?

1. dan815

it depends do u want it to mean anything

2. anonymous

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

3. pujan20

@dan815 i agree with fbi2015

4. dan815

who says its d^2y/dt^2

5. anonymous

well if x is time

6. Empty

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

7. imqwerty

wait a sec i got the answer :)

8. Empty

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

9. anonymous

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

10. ikram002p

@dan815 yeah it mean something in complex maybe xD

11. dan815

|dw:1440371299983:dw|

12. 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

13. Empty

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

14. dan815

i see

15. Empty

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

16. dan815

maybe in complex plane

17. dan815

like what does it mean to have complex routes

18. dan815

roots*

19. 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

20. 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

21. dan815

maybe something similiar to that is happening here

22. Empty

Yeah that looks good

23. 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

24. dan815

the way the 2nd derivate behaves in this case*

25. dan815

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

26. dan815

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

27. dan815

|dw:1440372327851:dw|

28. 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?

29. dan815

ya that makes sense

30. dan815

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

31. 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

32. dan815

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

33. dan815

im not really satisfied with that lol but ya

34. dan815

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

35. dan815

|dw:1440373563511:dw|

36. dan815

|dw:1440373638686:dw|

37. Empty

Hmmm I don't really understand what you mean

38. dan815

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

39. dan815

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

40. 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?

41. dan815

42. dan815

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

43. dan815

i dunno =.=

44. 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.

45. dan815

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

46. Empty

Me, I say that they aren't

47. dan815

lol

48. Empty

lol

49. dan815

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

50. dan815

what if these will have uses later then

51. 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.

52. dan815

53. dan815

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

54. dan815

okay well the way i see it is that

55. dan815

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

56. dan815

but we can pick other lines for other functions

57. 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

58. dan815

im just saying random stuff right now :>

59. 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

60. Empty