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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    I found the y value one critical point to be y=1/3x^2

  2. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    i got y^2=1/3x for the DM/dy

  4. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    whoops, I messed up the derivative

  6. anonymous
    • 5 years ago
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    even after i corrected my derivative, I still have a lot of nasty algebra...

  7. anonymous
    • 5 years ago
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    I know its pretty gross.

  8. anonymous
    • 5 years ago
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    I got 6y^7+4y^2-1=0

  9. anonymous
    • 5 years ago
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    did you get anything like that?

  10. anonymous
    • 5 years ago
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    I got 6yx^2 - 2=0 and I can't get the right x value when solving

  11. anonymous
    • 5 years ago
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    how did you get 6yx^2 -2...was that your DM/dy?

  12. anonymous
    • 5 years ago
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    from this I got the x value \[\sqrt{1/3x^2}\]

  13. anonymous
    • 5 years ago
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    That is my DM/dy

  14. anonymous
    • 5 years ago
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    DM/dy I got 6xy^2-2 as the y was cubed in the original problem, or is that a typo?

  15. anonymous
    • 5 years ago
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    OH whoops. that's what I got. I meant to square the y not the x. you're right

  16. anonymous
    • 5 years ago
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    I will try some factors then, but I don't see any off hand that work immediately.

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