Chapter 4.2, Problem 91E

Production: point of diminishing returns. A T-shirt manufacturer is planning to expand its workforce. It estimates that the number of T-shirts produced by hiring x new workers is given by

     $\begin{array}{cccc}T(x)& =& -0.25x^4+5x^3& 0\le x\le 15\end{array}$

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