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

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) $\left( - 2 , - \frac { 1 } { 3 } \right)$ , $\left( 1 , \frac { 59 } { 12 } \right)$