anonymous
  • anonymous
Find all points on the curve x^2 * y^2 + xy = 2 where the slope of the tangent line is -1.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
I got the derivative already: y' = (-2xy^2 - y)/(2x^2 * y + x) ...=-1 so how do I solve for those points?
anonymous
  • anonymous
right coulda guessed that much and
inkyvoyd
  • inkyvoyd
I think you substitute -1 for all values of y.

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inkyvoyd
  • inkyvoyd
Then you solve. I think. Check your answers afterwards to see it I was right.
inkyvoyd
  • inkyvoyd
*y' I mean
inkyvoyd
  • inkyvoyd
for all values of y', we should have -1
anonymous
  • anonymous
right
inkyvoyd
  • inkyvoyd
wait, I figured it out for a circle.
inkyvoyd
  • inkyvoyd
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
inkyvoyd
  • inkyvoyd
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