Chapter 4.2, Problem 87E

Revenue. The marketing research department of a computer company used a large city to test market the firm’s new laptop. The department found that the relationship between price p (dollars per unit) and the demand x (units per week) was given approximately by

     $\begin{array}{cccc}p& =& 1,296-0.12x^2& 0<x<80\end{array}$

So weekly revenue can be approximated by

     $\begin{array}{cccccc}R(x)& =& xp& =& 1,296x-0.12x^3& 0<x<80\end{array}$

1. (A) Find the local extrema for the revenue function.
2. (B) On which intervals is the graph of the revenue function concave upward? Concave downward?