#### natHenderson

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- Thread starter natHenderson
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If I were to do this problem, I would first use wolframalpha.com toView attachment 19159

I don't even know where to begin with this problem, can anybody help?

r = f(Θ) = Θ^3 - 6*Θ^2 + 9*Θ

That will let you analyze the position of the particle.

If you get stuck somewhere, come back and tell us exactly where you are stuck....

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r(t) = t^3 - 6t^2 + 9t

Do you know how to use calculus, to find the intervals where distance r(t) is increasing, while 0 ≤ t ≤ 2pi seconds?

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Yes. A function increases when its first derivative (rate-of-change, or slope) is positive.… is D the correct answer?

The first derivative of r is an easily-factored quadratic polynomial.

So, it's easy to determine intervals where the parabola lies above the horizontal axis. That serves as a check, for answer D.

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