Find All Points (If Any) of Horizontal and Vertical Tangency $x = t + 6 , y = t ^ { 3 } - 27 t$

Multiple Choice

Find all points (if any) of horizontal and vertical tangency to the curve $x = t + 6 , y = t ^ { 3 } - 27 t$

A) horizontal tangents: $( 9 , - 54 ) , ( 3,54 )$ , vertical tangent: none
B) horizontal tangent: none, vertical tangents: $( 9 , - 54 ) , ( 3,54 )$
C) horizontal tangents: $( 9,54 ) , ( 3,54 )$ , vertical tangent: none
D) horizontal tangent: none, vertical tangents: $( 9,54 ) , ( 3,54 )$
E) horizontal tangent: none, vertical tangent: none