- The curve \(C\) has equation
$$x ^ { 2 } + x y + y ^ { 2 } - 4 x - 5 y + 1 = 0$$
- Use implicit differentiation to find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
- Find the \(x\) coordinates of the two points on \(C\) where \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 0\)
Give exact answers in their simplest form.
(Solutions based entirely on graphical or numerical methods are not acceptable.)