The function below is the function of an initial public offering, or IPO. This is a brand new stock. 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 for a class of IPOs predicts the percent overvaluation of a stock as a function of time as: $R(t)=(t+2{)}^2*(t-2)*(t-4)+100$

Where $R(t)$ is the overvaluation in percent and $t$ is the time in months after the initial issue.

a$.$ Use the information provided by the first derivative, second derivative, and the 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 maximum$/$minimum$),$ and any false signals prior to a horizontal asymptote. Explain your reasoning.

b$.$ Make a sketch of the function without using your graphing calculator.