Forecasting Profits As a result of increasing energy costs, the growth rate of the profit of a 4-year old
glassblowing company has begun to decline. The company's management, after consulting with energy experts,
decides to implement certain energy-conservation measures aimed at cutting energy bills. The general manager
reports that, according to his calculations, the growth rate of their profit should be on the increase again within
4 years. If the glassblowing company's profit (in hundreds of dollars) t years from now is given by the function
$P(t) = t^3 - 15t^2 + 20t + 50$ $(0 \le t \le 8)$
determine whether the general manager's forecast will be accurate. Hint: Find the inflection point of the function $P$
and study the concavity of $P$.
Yes, the forecast will be accurate.
No, the forecast will not be accurate.
