15. Sketch y = f (x). Label completely. Properties are: No y intercept. Max at P(2, 2) Mins at Q(4, -1) and at R(-1, 2). Oblique asymptote y = x 1. lim f(x) = 0, lim f(x) = 00 , x>oo x>3' xgjm = 00. Jirgx) = 00. item = -r 31:2. x) = 0 X: 3 and X: 0 are VA's. As x > 00, y > the oblique from below it. Application 16. The park across the street is to be treated to control a new algae that is growing on top of the grass. After t days of treatment the concentration of algae per square metre is given by A(t) = 251?2 3001: + 1200. Determine the lowest concentration of algae in the rst week after the treatment. Prove it is the lowest. [5 marks] 17. A lady who runs a warehouse has to deal with two large sound speakers that blare out a lot of noise, so she wants to place her desk optimally to minimize total sound. The speakers are 80 metres apart, but one has 3 times the volume of the other. She needs to place her desk in the right place for minimum sound. Because sound quality is inversely proportional to the square of the distance, the function that she needs to 3 (80x)2 where x is her distance from the smaller optimize is SOC) = x12 + speaker. Use Calculus to determine the value of x that minimizes 5. Round x to 2 decimal places and prove that this value produces a minimum using FDT. [7 marks]