anonymous
  • anonymous
Find all the critical points of the function M(x,y) = 2x^2 - x^3 + 2xy^3 - 2y.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
I found the y value one critical point to be y=1/3x^2
anonymous
  • anonymous
I'm having trouble finding the x value for this particular point and I'm not sure if there are any other critical points
anonymous
  • anonymous
i got y^2=1/3x for the DM/dy

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anonymous
  • anonymous
umm, as far as solving this, umm, the algebra is looking nasty. substitute this into the DM/dx and try to solve for actual numbers
anonymous
  • anonymous
whoops, I messed up the derivative
anonymous
  • anonymous
even after i corrected my derivative, I still have a lot of nasty algebra...
anonymous
  • anonymous
I know its pretty gross.
anonymous
  • anonymous
I got 6y^7+4y^2-1=0
anonymous
  • anonymous
did you get anything like that?
anonymous
  • anonymous
I got 6yx^2 - 2=0 and I can't get the right x value when solving
anonymous
  • anonymous
how did you get 6yx^2 -2...was that your DM/dy?
anonymous
  • anonymous
from this I got the x value \[\sqrt{1/3x^2}\]
anonymous
  • anonymous
That is my DM/dy
anonymous
  • anonymous
DM/dy I got 6xy^2-2 as the y was cubed in the original problem, or is that a typo?
anonymous
  • anonymous
OH whoops. that's what I got. I meant to square the y not the x. you're right
anonymous
  • anonymous
I will try some factors then, but I don't see any off hand that work immediately.

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