1. [T marks] Find the value of the constants c, b, and c (a 72 0) so that the graph of the function f(:1?) = 1532 + bi: + c has a local maximum at (5.12} and crosses the y-acxis at (0, 3). 2. [14 marks] . . . . 2:2 3:: + 6 Use the Algorithm for Curve Sketchmg for Rational Functions to sketch f (:11) = T. Show all steps and label the points on the graph. 3. [6 marks] . . . . . ++m . . . The Intensity of a beam of llght 1s green by t) = \"2, where t is the tlme in seconds. Determine the minimum intensity of light during the period 0 :1 t S 14. 4. [9 marks] A theatre company averages 2000 patrons per performance. The company charges patrons $7.00 each to attend a performance. The results of a survey show that 40 fewer people would attend a performance for each $0.10 increase in the cost (and 40 more people would attend a performance for each $0.10 decrease in the cost.) What price per patron should the company charge in order to maximize revenue if they want at least 1560 patrons per performance and the capacity of the theatre is 2640 patrons