Given $\mathbf { r } ( t ) = 3 t ^ { 2 } \mathbf { i } + 4 t ^ { 3 } \mathbf { j }$
a. Find $\mathbf { r } ( - 1 )$ and $\mathbf { r } ^ { \prime } ( - 1 )$ .
b. Sketch the curve defined by r and the vectors $\mathbf { r } ( - 1 )$ and $\mathbf { r } ^ { \prime } ( - 1 )$ on the same set of axes.

Question

Given $\mathbf { r } ( t ) = 3 t ^ { 2 } \mathbf { i } + 4 t ^ { 3 } \mathbf { j }$ 
a. Find $\mathbf { r } ( - 1 )$ and $\mathbf { r } ^ { \prime } ( - 1 )$ . 
b. Sketch the curve defined by r and the vectors $\mathbf { r } ( - 1 )$ and $\mathbf { r } ^ { \prime } ( - 1 )$ on the same set of axes.

Quizplus · Accepted Answer

The Answer of Given $\mathbf { r } ( t ) = 3 t ^ { 2 } \mathbf { i } + 4 t ^ { 3 } \mathbf { j }$ 
a. Find $\mathbf { r } ( - 1 )$ and $\mathbf { r } ^ { \prime } ( - 1 )$ . 
b. Sketch the curve defined by r and the vectors $\mathbf { r } ( - 1 )$ and $\mathbf { r } ^ { \prime } ( - 1 )$ on the same set of axes.

Given r(t)=3t2i+4t3j\mathbf { r } ( t ) = 3 t ^ { 2 } \mathbf { i } + 4 t ^ { 3 } \mathbf { j }r(t)=3t2i+4t3j

Given $\mathbf { r } ( t ) = 3 t ^ { 2 } \mathbf { i } + 4 t ^ { 3 } \mathbf { j }$