Find parametric equations for the tangent line to the curve with parametric equations $x = 3 t$ $y = 7 t ^ { 2 }$ $z = 8 t ^ { 3 }$ at the point with $t = 1$
A) $x = 3 + 3 t$ $y = 7 + 14 t$ $z = 8 + 24 t$
B) $x = 1 + 3 t$ $y = 1 + 14 t$ $z = 1 + 24 t$
C) $x = 1 + 3 t$ $y = 1 + 7 t$ $z = 1 + 8 t$
D) $x = 3 + 3 t$ $y = 7 + 7 t$ $z = 8 + 8 t$

Question

Quizplus · Accepted Answer

The tangent line at $t = 1$ is found using the derivatives of the parametric equations: $dx/dt = 3$, $dy/dt = 14t$, $dz/dt = 24t^2$. At $t = 1$, the point is $(3, 7, 8)$ and the direction vector is $(3, 14, 24)$. The parametric equations are $x = 3 + 3t$, $y = 7 + 14t$, $z = 8 + 24t$.

Find Parametric Equations for the Tangent Line to the Curve x=3tx = 3 tx=3t

Find Parametric Equations for the Tangent Line to the Curve $x = 3 t$