Find the highest point on the graph of $$4 x^2 + 3 x y + 7 y^2 = 14$$

We begin by computing $\frac{dy}{dx}$ implicitly for points $(x,y)$ on the graph, obtaining:
$\displaystyle\frac{dy}{dx} =$
List the critical points, in increasing order, writing DNE when you run out of critical points
$x_1 =$
$x_2 =$
$x_3 =$
$x_4 =$
Thus the highest point on the graph is
$(x,y)= ($ $,$$)$