# Slope of a Curve of Given Parametric Equations

**Problem**

A point moves in the plane according to equations *x* = *t*^{2} + 2*t* and *y* = 2*t*^{3} - 6*t*. Find *dy*/*dx* when *t* = 0, 2, 5.

A. -3, -3, -12 | C. 3, 3, 12 |

B. 3, -3, 12 | D. -3, 3, 12 |

**Answer Key**

[ D ]

**Solution**

$x = t^2 + 2t$

$dx = (2t + 2) \, dt$

$y = 2t^3 - 6t$

$dy = (6t^2 - 6) \, dt$

$\dfrac{dy}{dx} = \dfrac{(6t^2 - 6)\,dt}{(2t + 2)\,dt}$

$\dfrac{dy}{dx} = \dfrac{3t^2 - 3}{t + 1}$

When *t* = 0, *dy*/*dx* = -3

When *t* = 2, *dy*/*dx* = 3

When *t* = 5, *dy*/*dx* = 12

Answer: [ D ]

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