Calculus- answer check

A brand new stock is also called an initial public offering. This model predicts the percent overvaluation of a stock as R(t)=9t((t-3)^3/2.718) where is the overvaluation in percent and t is the time in months after the initial issue.

Use the information provided by the first derivative, second derivative to find the inflection point, the local maximum/minimum, and any false signals.

I figured out that the first derivative is R't=9/2.718(t-4)^2 (4t-4) and the second one is R"(t)=9/2.718(t-4)(12t-24). Would the inflection point be at (4,0) and would the local min be at (1,-89.4)? there also wouldnt be a local max right? Also, what are false signals?

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asked by Liz
  1. Since R"=0 at t=2 and t=4, I see two inflection points.

    R'=0 at t=1 and t=4. Since R' and R" are both zero at t=4 (because of the multiple root there), there is no max/min at t=4. At R"(1)>0, so that's a local minimum.

    Not sure about the false signals. I'm sure you can google the terms used in investing, and get many explanations. Just off hand, I'd say that the inflection point at t=4 would be such a signal. The stock price has been rising, but slowing down, and appears ready to fall, but selling would be a bad idea, since it's poised to take off again.

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    posted by Steve

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