Chapter 4.2, Problem 92E

Production: point of diminishing returns. A baseball cap manufacturer is planning to expand its workforce. It estimates that the number of baseball caps produced by hiring x new workers is given by

     $\begin{array}{cccc}T(x)& =& -0.25x^4+6x^3& 0\le x\le 18\end{array}$

When is the rate of change of baseball cap production increasing and when is it decreasing? What is the point of diminishing returns and the maximum rate of change of baseball cap production? Graph T and T′ on the same coordinate system.