Chapter 14, Problem 39RE

Instantaneous Rate of Change The following data represent the revenue $R$(in dollars) received from selling $x$ wristwatches at Wilk’s Watch Shop.

$\begin{array}{cc}\text{Wristwatches,}x& \text{Revenue},R\\ 0& 0\\ 25& 2340\\ 40& 3600\\ 50& 4375\\ 90& 6975\\ 130& 8775\\ 160& 9600\\ 200& 10000\\ 220& 9900\\ 250& 9375\end{array}$

Find the average rate of change of revenue from $x=25$ to $x=130$ wristwatches.

Find the average rate of change of revenue from $x=25$ to $x=90$ wristwatches.

Find the average rate of change of revenue from $x=25$ to $x=50$ wristwatches.

Using a graphing utility, find the quadratic function of best fit.

Using the function found in part (d), determine the instantaneous rate of change of revenue at $x=25$ wristwatches.