Consider the function \(F(x,y) = x^2y-xy^2+4\). A representation of several curves are given below. Select all that are a part of a level curve of \(F(x,y)\).

\(y=x\) \(y=2x\) \(x^2y-xy^2=7\) \(\vec {r}(t) =\vector {0,5t^2+1}\) \(\vec {r}(t) =\vector {4t,4t}\) \(\vec {r}(t)=\vector {7,t}\)
Evaluate \(F(x,y)\) along each given curve. For example, along \(y=2x\), \(F(x,y)=F(x,2x)\) (since \(y=2x\)) so
\[ F(x,2x) = x^2(2x)-x(2x)^2+4 = \answer {-2}x^3+4. \]
Since \(F(x,y)\) is constantnot constant along the curve \(y=2x\), this curve isis not part of a level curve of \(F(x,y)\).