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calyne

Find all points on the curve x^2 * y^2 + xy = 2 where the slope of the tangent line is -1.

  • 2 years ago
  • 2 years ago

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  1. calyne
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    I got the derivative already: y' = (-2xy^2 - y)/(2x^2 * y + x) ...=-1 so how do I solve for those points?

    • 2 years ago
  2. calyne
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    right coulda guessed that much and

    • 2 years ago
  3. inkyvoyd
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    I think you substitute -1 for all values of y.

    • 2 years ago
  4. inkyvoyd
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    Then you solve. I think. Check your answers afterwards to see it I was right.

    • 2 years ago
  5. inkyvoyd
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    *y' I mean

    • 2 years ago
  6. inkyvoyd
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    for all values of y', we should have -1

    • 2 years ago
  7. calyne
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    right

    • 2 years ago
  8. inkyvoyd
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    wait, I figured it out for a circle.

    • 2 years ago
  9. inkyvoyd
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    x^2+y^2=sqrt(2) 2x+2yy'=0 y'=-1 because the slope=-1 2x-2y=0 x=y so we have to equations x=y x^2+y^2=sqrt2

    • 2 years ago
  10. inkyvoyd
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    |dw:1333951610523:dw|

    • 2 years ago
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