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

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Definitions:

Red Income

This term is also not recognized in standard economic discussions and might be used in a specific context that is not universally defined.

Ambrosia

Often referred to in ancient texts, ambrosia is described as a divinely nourishing substance associated with immortality.

Blue Income

Similar to "Red Income," this term does not have a recognized definition in economics and likely pertains to a specific, non-standard use.

Ambrosia

In mythology, it is the food or drink of the gods, thought to confer immortality, but in a general context, it refers to something very pleasing to taste or smell.