Question

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

Answer 1

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

Answer 2

right coulda guessed that much and

Answer 3

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

Answer 4

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

Answer 5

*y' I mean

Answer 6

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

Answer 7

right

Answer 8

wait, I figured it out for a circle.

Answer 9

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