Kinematics position function question

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SUMMARY

The discussion centers on solving a kinematics problem involving the position function X = (t^3 - 3t^2 + 6t) meters, where t represents time in seconds. The user seeks to determine the position of a particle at its minimum speed after t = 0. The approach of factoring and using the quadratic formula led to imaginary roots, indicating a need for a different method to find the critical points of the function.

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< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >[/color]

I'm studying for AP test. This is not a homework question. Does anyone know how to do number 2? I don't even know where to start. I tried factoring out t and using quadratic formula, but I kept getting imaginary roots and t can't equal zero.

X = (t^3 - 3t^2 + 6t)m

where m is meters and t is seconds.
What is the position of the particle when it is at its minimum speed (after t = 0)

thanks in advance for anyone that answers.
 

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