Answer
Slope = $\sqrt{3}$
Work Step by Step
We apply implicit differentiation and solve for $\frac{dy}{dx}$:
$x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4$
$\frac{2}{3}x^{-\frac{1}{3}} +\frac{2}{3}y^{-\frac{1}{3}} * \frac{dy}{dx}=0$
$\frac{dy}{dx} = -(\frac{x}{y})^{-\frac{1}{3}}$
$\frac{dy}{dx}|_{(-1,3\sqrt{3})} = -(\frac{-1}{3\sqrt{3}})^{-\frac{1}{3}} = \sqrt{3}$
