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Compute each part of given problem:
Problem: A particle moves along the x-axis according to the equation x(t) = 2.0 + 3.0t2 at - 1.0t3, where x is in meters and t is in seconds.
Part I: What is the position of this particle when it achieves its maximum speed in the positive x-direction?
Part II: What is its speed at that time?
Please show solution step by step with detailed explanation.
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