Chapter 4.2, Problem 94E

Advertising: point of diminishing returns. A company estimates that it will sell N(x) units of a product after spending $x thousand on advertising, as given by

     $\begin{array}{cccc}N(x)& =& -0.5x^4+26x^3-360x^2+20,000& 15\le x\le 24\end{array}$

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