posted by Fredrick E. .
find all points on the curve x^2y^2+xy=2 where the slope of the tangent line is -1
I know that you have to find the derivative when it equals -1
(i don't know if it is correct or not)
but i don't know how to go from here. any help would be good
try changing variables. let z=xy in the origianal equation, solve for z
z=1 or -2 or z is a constant.
Then z=xy or
y=-x and xy=-1 or 1
x=sqrt2, y=-x =-sqrt2
check: original line 4-2=2 checks.
check: originalline 1=1=2 checks.
PointB: x=sqrt2, y=-sqrt2
Can you explain using implicit differention?
No, I tried it that way, it bogged down in a third degree equation after I substituted, so I gave up that way.