Find the Curvature of the Curve R(t) $$r ( t ) = ( 2 t + 6 ) i - 4 j + \left( 8 - 1 t ^ { 2 } \right) \mathbf { k }$$

Multiple Choice

Find the curvature of the curve r(t) .
- $$r ( t ) = ( 2 t + 6 ) i - 4 j + \left( 8 - 1 t ^ { 2 } \right) \mathbf { k }$$

A) $k = \frac { 1 } { 2 \sqrt { 1 + t ^ { 2 } } }$
B) $\kappa = 2 \sqrt { 1 + t ^ { 2 } }$
C) $\kappa = 2 \left( 1 + t ^ { 2 } \right) ^ { 3 / 2 }$
D) $\kappa = \frac { 1 } { 2 \left( 1 + t ^ { 2 } \right) ^ { 3 / 2 } }$