The position of a particle moving along the x-axis is defined by the equation x = 4.7t² − 3.2t³. To determine the position when the particle achieves its maximum speed in the positive x-direction, one must first calculate the velocity by differentiating the position function with respect to time, yielding v(t) = 9.4t - 9.6t². Setting this velocity equation to zero allows for the identification of critical points, which can then be analyzed to find the maximum speed. The position at this maximum speed can be calculated by substituting the time value back into the original position equation.
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