Consider the graph of x^2+xy+y^2=1. Use implicit differentiation to find all points on the graph where the tangent line is parallel to the line y=-x.
Where do I go after I implicitly differentiate this thing?
2x+y'+2y*y'=0
y'+2y*y'=-2x
y'(1+2y)=-2x
y'=-(2x)/(1+2y)
Did I do that right?
Hello, ebonyscythe!
Your differentiation is off . . .
Consider the graph of
Use implicit differentiation to find all points on the graph
where the tangent line is parallel to the line
. .
Then we have: .
Factor: .
. . Hence: .
Set: .
Substitute into [1]: .
. . Then: .
Answers: .