Find parametric equations for the tangent line to the curve with parametric equations $x = 2 t$ $y = 7 t ^ { 2 }$ $z = 4 t ^ { 3 }$ at the point with $t = 1$
A) $x = 2 + 2 t$ $y = 7 + 14 t$ $z = 4 + 12 t$
B) $x = 2 + 2 t$ $y = 7 + 7 t$ $z = 4 + 4 t$
C) $x = 1 + 2 t$ $y = 1 + 7 t$ $z = 1 + 4 t$
D) $x = 1 + 2 t$ $y = 1 + 14 t$ $z = 1 + 12 t$

Question

Quizplus · Accepted Answer

The derivatives of the parametric equations at $t = 1$ give the direction vector of the tangent line: $\frac{dx}{dt} = 2$, $\frac{dy}{dt} = 14$, $\frac{dz}{dt} = 12$. The point at $t = 1$ is $(2, 7, 4)$. Thus, the parametric equations for the tangent line are $x = 2 + 2t$, $y = 7 + 14t$, $z = 4 + 12t$.

Find Parametric Equations for the Tangent Line to the Curve x=2tx = 2 tx=2t

Find Parametric Equations for the Tangent Line to the Curve $x = 2 t$