Wolfram alpha is telling me there isn't. I guess this reduces down to finding the inflection point in some way and testing against points A and D.
Here's the equation I'm using.
$$
x=(1-t)^3*A_{x}+3*((1-t)^2)*t*B_{x}+3*(1-t)*(t^2)*C_{x}+(t^3)*D_{x}
$$
$$
y=(1-t)^3*A_{y}+3*((1-t)^2)*t*B_{y}+3*(1-t)*(t^2)*C_{y}+(t^3)*D_{y}
$$