# Determine the x-y coordinates of the points where the following parametric equations will have horizontal or vertical tangents x=t^3-3ty=3t^2-9

Determine the x-y coordinates of the points where the following parametric equations will have horizontal or vertical tangents $x={t}^{3}-3t$
$y=3{t}^{2}-9$
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Szeteib
$x={t}^{3}-3t$
$y=3{t}^{2}-9$
$\frac{dy}{dx}=\frac{6t}{3{t}^{2}-3}$
for horizontal tangent $\frac{dy}{dx}=0⇒t=0,P\left(0,-9\right)$
For verticle tangent $\frac{dy}{dx}=\mathrm{\infty }ot\frac{dy}{dx}=\frac{1}{0}$
$\frac{6t}{3{t}^{2}-3}=\frac{1}{0}⇒t=±1$
$P\left(-2,-6\right)\varphi \left(2,-6\right)$