Financial analysts use graphical models to predict stock values for a new stock. A brand new stock is also called an IPO (initial public offering). When a stock is first issued it sells for more than it is really worth. One model for a class of Internet IPO's predicts the percent overvaluation of a stock as a function of time as R(t) = 250[(t²/2.718^3t)], where R(t) is the overvaluation in percent and t is the time in months after the initial issue of the stock.

1. Use the information provided by the first derivative, second derivative and asymptotes 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 max/min) and any false signals prior to a horizontal asymptote. Explain your reasoning.
2. Make a sketch without using a graphing calculator. Show all the steps your used to sketch it with accuracy.