## anonymous 5 years ago Find all the critical points of the function M(x,y) = 2x^2 - x^3 + 2xy^3 - 2y.

1. anonymous

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

2. 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

3. anonymous

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

4. 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

5. anonymous

whoops, I messed up the derivative

6. anonymous

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

7. anonymous

I know its pretty gross.

8. anonymous

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

9. anonymous

did you get anything like that?

10. anonymous

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

11. anonymous

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

12. anonymous

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

13. anonymous

That is my DM/dy

14. anonymous

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

15. anonymous

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

16. anonymous

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

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