Find the Points on the Curve $x ( t ) = \frac { t ^ { 3 } } { 1 + t } , y ( t ) = \frac { 1 } { 1 + t }$

Multiple Choice

Find the points on the curve $x ( t ) = \frac { t ^ { 3 } } { 1 + t } , y ( t ) = \frac { 1 } { 1 + t }$ where the tangent line is vertical.

A) $\left( \frac { 27 } { 4 } , - 2 \right)$
B) $( 0,1 ) , \left( \frac { 27 } { 4 } , - 2 \right)$
C) $( 0,1 )$
D) $( 0,1 ) , \left( \frac { 27 } { 4 } , 2 \right)$
E) $( 0,1 ) , \left( - \frac { 27 } { 4 } , 2 \right)$