Let $y$ be defined implicitly by the equation $\ln(3 y) = 4 xy$. Use implicit differentiation to find the first derivative of $y$ with respect to $x$.

$\displaystyle \frac{dy}{dx} =$

Use implicit differentiation to find the second derivative of $y$ with respect to $x$.

$\displaystyle \frac{d^2y}{dx^2} =$

Note: Your answer should only involve the variables $x$ and $y$. You should simplify your answer as much as possible before entering it into WeBWorK.

Find the point on the curve where $\displaystyle \frac{d^2y}{dx^2} = 0$.

$\displaystyle \frac{d^2y}{dx^2} = 0$ at the point $(x,y) = ($ $)$.