#### Answer

$\frac{dy}{dt}=\frac{-3}{14}$

#### Work Step by Step

$4x^{3} - 6xy^{2}+3y^{2}= 228$
$12x^{2}\frac{dx}{dt} -12xy\frac{dy}{dt} -6y^{2}\frac{dx}{dt}+6y\frac{dy}{dt}=0$
$(6y-12xy)\frac{dy}{dt}+(12x^{2}-6y^{2})\frac{dx}{dt}=0$
Now substitute x = -3, y = 4, and dx/dt =3 to get
$\frac{dy}{dt}=\frac{-3}{14}$