Question

find any point (a,b) on the curve x^2+xy=2y-8 where the tangent line at the point is vertical?

Answer 1

take the derivative and find where it is undefined

Answer 2

\[x^2+xy=2y-8\]
\[2x+y+xy'=2y'\] solve for \(y'\)

Answer 3

\[2x+y=2y'-xy'\]
\[2x+y=(2-x)y'\]
\[\frac{2x+y}{2-x}=y'\] undefined if \(x=2\)