Find the point(s) (if any) of horizontal tangent lines for the equation #x^2+xy+y^2=6#. If none exist, why?
1 Answer
Nov 11, 2016
graph{(x^2+xy+y^2-6)((x-sqrt2)^2+(y+2sqrt2)^2-0.01)((x+sqrt2)^2+(y-2sqrt2)^2-0.01)=0 [-8.89, 8.89, -4.444, 4.445]}
Explanation:
Implicitly differentiating over x the equation we get (using y'=
So
So
Now intersect with the equation