Given $\mathbf { r } ( t ) = 7 t ^ { 2 } \mathbf { i } + 4 t ^ { 3 } \mathbf { j }$

Essay

Given $\mathbf { r } ( t ) = 7 t ^ { 2 } \mathbf { i } + 4 t ^ { 3 } \mathbf { j }$ .
a. Find $\mathbf { r } ( - 1 )$ and $\mathbf { r } ^ { \prime } ( - 1 )$ .
b. Sketch the curve defined by $\mathbf { r }$ and the vectors $\mathbf { r } ( - 1 )$ and $\mathbf { r } ^ { t } ( - 1 )$ on the same set of axes.