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How do I Determine using algebraic analysis, the movement of a particle when its going in a negative and positive direction, and at rest. relevant

How do I Determine using algebraic analysis, the movement of a particle when its going in a negative and positive direction, and at rest.

relevant info: s(t)=t⁴-6t³+4t²+3 & v(t)= 4t³ -18t²+8t

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