Chapter 2 - The Derivative - 2.7 Implicit Differentiation - Exercises Set 2.7 - Page 166: 28

Slope = $0$

We use implicit differentiation: $y^3 + yx^2 + x^2 -3y^2 = 0$ $3y^2 \frac{dy}{dx} + x^2 * \frac{dy}{dx} + 2xy + 2x - 6y * \frac{dy}{dx} = 0$ $(3y^2 -6y+x^2) \frac{dy}{dx} = -2x-2xy$ $ \frac{dy}{dx} = \frac{-2x-2xy}{3y^2-6y+x^2}$ $ \frac{dy}{dx}|_{(0,3)} = 0$