Calculus

A brand new stock is also called an initial public offering. In this model, the period immediately after the stock is issued offers excess returns on the stock—that is, the stock is selling for more than it is really worth. One such model predicts the percent overvaluation of a stock as R(t)=9t((t-3)^3/2.718)

where R 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 prepare advice for clients as to when they should expect a signal to prepare to buy or sell (inflection point), the exact time when they should buy or sell (local maximum/minimum), and any false signals. Explain your reasoning.

Would the first derivative be R'(t)=3.311258278(3(t-4)^2(t)+(t-4)^3) and the second derivative be R''(t)=3.311258278(6(t-4)x+6(t-4)^2)?

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asked by Liz
  1. The way you typed R(t), we have to read it as

    R(t) = 9/2.718 ( t(t-3)^3)

    then R' (t) = (9/2.718) [ t (3)(t-3)^2 + (t-3)^3 ]
    = (500/151)(t-3)^2 ( 3t + t-3)
    = (500/151)(4t - 3)(t-3)^2

    How did the base of (t-3) suddenly turn into (t-4) ?

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    posted by Reiny
  2. Sorry about that. It looks like thins:

    R(t)= 9t[(t-4)^3/2.718]

    The 9t is on the outside without a denominator

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    posted by Liz

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