1.. Recall the problem introduced at the start of this section: The manager of a miniature golf course is planning to raise the ticket price per game. At the current price of $6.50, an average of 81 rounds is played each day. The manager's research suggests that for every $0.50 increase in price, an average of four fewer games will be played each day. The revenue, R, in dollars, from sales an be modelled by the function R(n) = (81 - 4n)(6.50 + 0.50n), where n represents the number of $0.50 increases in the price. By nding the derivative, the manager can determine the price that will provide the maximum revenue. I) Describe two methods that could be used to determine R'(n). Apply your methods and then compare the answers. Are they the same? b) Evaluate R'(4). What information does this value give the manager? 6 Determine when R'tn) = 0. What information does this give the manager? I) Sketch a graph of R(n). Determine the maximum revenue from the graph. Compare this value to your answer in part c). What do you notice? I) Describe how the derivative could be used to find the value in part d)