Chapter 4.2, Problem 7MP

Matched Problem 7 Repeat example 7 for

     $\begin{array}{cc}N\left(x\right)=4x^3-0.25x^4+500& 0\le x\le 12\end{array}$

Maximum Rate of Change Currently, a discount appliance store is selling 200 large-screen TVs monthly. If the store invests $x thousand in an advertising campaign, the ad company estimates that monthly sales will be given by

$\begin{array}{cc}N\left(x\right)=3x^3-0.25x^4+200& 0\le x\le 9\end{array}$

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.