Find $\frac{dy}{dx}$ when $t=0$ for $\begin{cases}x = t^2 + 2t \\ y = 2t^3 - 6t\end{cases}$

Question

A dot is moving on a grid following this rule: $$\begin{cases}x = t^2 + 2t \\ y = 2t^3 - 6t\end{cases}$$ I need to find $\frac{dy}{dx}$ when $t =0$.

It seems like I should use implicit differentiation, but I'm not sure how to apply it.

Answer 1

$$ x = t² + 2t, y = 2t³ - 6t $$

$$dx/dt= 2t + 2,$$ $$dy/dt= 6t²-6$$

You want $dy/dx$ for $t=0$. Just use algebra:

$$(6t²-6) /( 2t+2)$$ for t=0, then $$dy/dx=-6/2=-3.$$