Chapter 4.2, Problem 93E

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

     $\begin{array}{cccc}N(x)& =& -0.5x^4+46x^3-1,080x^2+160,000& 24\le x\le 45\end{array}$

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.