Answer
$$K = 0$$
Work Step by Step
$$\eqalign{
& {\bf{r}}\left( t \right) = 4t{\bf{i}} - 2t{\bf{j}},{\text{ at }}t = 1 \cr
& {\text{By Theorem 12}}{\text{.8 }} \cr
& {\text{If }}C{\text{ is a smooth curve given by }}{\bf{r}}\left( t \right),{\text{ then the curvature }}K{\text{ of}} \cr
& C{\text{ at }}t{\text{ is }}K = \frac{{\left\| {{\bf{r}}'\left( t \right) \times {\bf{r}}''\left( t \right)} \right\|}}{{{{\left\| {{\bf{r}}'\left( t \right)} \right\|}^3}}} \cr
& {\bf{r}}\left( t \right) = 4t{\bf{i}} - 2t{\bf{j}} \cr
& {\bf{r}}'\left( t \right) = 4{\bf{i}} - 2{\bf{j}} \cr
& {\bf{r}}''\left( t \right) = 0 \cr
& {\bf{r}}'\left( t \right) \times {\bf{r}}''\left( t \right) = 0 \cr
& {\text{Therefore,}} \cr
& K = \frac{{\left\| {{\bf{r}}'\left( t \right) \times {\bf{r}}''\left( t \right)} \right\|}}{{{{\left\| {{\bf{r}}'\left( t \right)} \right\|}^3}}} = \frac{0}{{{{\left\| {4{\bf{i}} - 2{\bf{j}}} \right\|}^3}}} \cr
& K = 0 \cr} $$
