Question

Find all the critical points of the function M(x,y) = 2x^2 - x^3 + 2xy^3 - 2y.

Answer 1

I found the y value one critical point to be y=1/3x^2

Answer 2

I'm having trouble finding the x value for this particular point and I'm not sure if there are any other critical points

Answer 3

i got y^2=1/3x for the DM/dy

Answer 4

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

Answer 5

whoops, I messed up the derivative

Answer 6

even after i corrected my derivative, I still have a lot of nasty algebra...

Answer 7

I know its pretty gross.

Answer 8

I got 6y^7+4y^2-1=0

Answer 9

did you get anything like that?

Answer 10

I got 6yx^2 - 2=0 and I can't get the right x value when solving

Answer 11

how did you get 6yx^2 -2...was that your DM/dy?

Answer 12

from this I got the x value \[\sqrt{1/3x^2}\]

Answer 13

That is my DM/dy

Answer 14

DM/dy I got 6xy^2-2 as the y was cubed in the original problem, or is that a typo?

Answer 15

OH whoops. that's what I got. I meant to square the y not the x. you're right

Answer 16

I will try some factors then, but I don't see any off hand that work immediately.