APFIVE The function $$P(t) = t^3 - 4t^2 + 3t + 1$$ models the rate of change, in hundreds of people per hour, of the number of people in a shopping center for time $$t$$ hours, where $$0 \leq t \leq 2$$. Which of the following gives the time $$t$$ and the reasoning for when the number of people in the shopping center is at a maximum?
$$t = 1.445$$, because the rate of change in the number of people inside the shopping center changes from positive to negative.
$$t = 0.451$$, because the rate of change in the number of people inside the shopping center changes from increasing to decreasing.
$$t = 0.451$$, because the rate of change in the number of people inside the shopping center changes from positive to negative.
$$t = 1.445$$, because the rate of change in the number of people inside the shopping center changes from increasing to decreasing.
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