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



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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?

calyne
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right coulda guessed that much and

inkyvoyd
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I think you substitute 1 for all values of y.

inkyvoyd
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Then you solve. I think. Check your answers afterwards to see it I was right.

inkyvoyd
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*y' I mean

inkyvoyd
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for all values of y', we should have 1

calyne
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right

inkyvoyd
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wait, I figured it out for a circle.

inkyvoyd
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x^2+y^2=sqrt(2)
2x+2yy'=0
y'=1 because the slope=1
2x2y=0
x=y
so we have to equations
x=y
x^2+y^2=sqrt2

inkyvoyd
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