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

question 24

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