The Tangent Line to the Curve Y = $\frac { 1 } { 6 }$

question 97

Multiple Choice

The tangent line to the curve y = $\frac { 1 } { 6 }$ $x ^ { 3 }$ - $\frac { 1 } { 4 }$ $x ^ { 2 }$ - x + 4 is perpendicular to the line $18 x + 9 y = - 37$ at two points on the curve. Find the two points.

• A) (2, 0), (-1, 0)
• B) \(\left( 2 , \frac { 7 } { 3 } \right)\) , \(\left. - 1 , \frac { 55 } { 12 } \right)\)
• C) \(\left( 2 , \frac { 7 } { 3 } \right)\) , \(\left.( 1 , \frac { 55 } { 12 } \right)\)
• D) \(\left( - 2 , - \frac { 1 } { 3 } \right)\) , \(\left( 1 , \frac { 59 } { 12 } \right)\)

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Definitions:

Asymmetric Information

A situation in which one party in a transaction has more or superior information compared to another, often leading to an unfair advantage.

Moral Hazard

The risk that one party to a transaction behaves in a way that is undesirable from the other party's point of view because the latter cannot effectively control the former.

Asymmetric Information

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Products that exceed the standard level of performance, durability, or finishing, often resulting in higher consumer satisfaction.