A Conservative Force on a Particle Moving Along the X $\overrightarrow { \mathbf { F } } = \left( 3 x ^ { 2 } - 2 x \right) \tilde{ \mathbf { i } }$

Multiple Choice

A conservative force on a particle moving along the x axis is given by $\overrightarrow { \mathbf { F } } = \left( 3 x ^ { 2 } - 2 x \right) \tilde{ \mathbf { i } }$ .Which of the following is a potential that is associated with this force?

A) $( 6 x - 2 ) \tilde{ \mathbf { i } }$
B) $( - 6 x + 2 ) \tilde{ \mathbf { i } }$
C) $x ^ { 3 } - x ^ { 2 } + 3$
D) $- x ^ { 3 } + x ^ { 2 } + 3$
E) No answer given above is correct.