1.

1. Consider the function f(x) = x3 + 6x2 + 9x. 0) Determine whether the function is even, odd, or neither. b) Determine the domain of the function. c) Determine the intercepts. d) Determine the critical points, intervals of increase! decrease, any extrema, intervals of concavity. and any points of inflection. e) Sketch a graph. 2. Analyze The. key features of The function f(x) = x4 - 5x3 + x2 + 21x - 18. Then use. your analysis to sketch a graph. 5x x2 + 4 ' a) How does the function behave as x > ice ? Explain your reasoning. b) Determine the intervals of increase/decrease and the coordinates of any local extrema. c) Determine the intervals of concavity and the coordinates of any points of inflection. d) Sketch a graph using your results from a) to c). 3. Consider the rational function f(x) = 4. Consider the function f(x) = x2 + 2x +3 x+1 a) How does the function f(x) behave as x -> too ? Explain your reasoning. b) What types of asymptotes does f(x) have? How can you tell just by looking at the equation? c) Determine the equations of the asymptotes. d) State the intercepts. e) Determine the intervals of increase/decrease and the coordinates of the local extrema. f) Determine the intervals of concavity and the coordinates of any points of inflection. 9) Sketch a graph.1 . A lifeguard has 200m of rope and some buoys with which she intends to enclose a rectangular area at a lake for swimming. The beach will form one side of the rectangle, the rope forms the other three sides. Find the dimensions that will produce the maximum enclosed area if a) there are no restrictions on the dimensions. b) due to the depth of the water, the area cannot extend more than 40m into the lake. 2. A cardboard box with a square base is to have a volume of 8L (or a capacity of 8000 cm3). a) Find the dimensions that will minimize the amount of cardboard to be used. b) The cardboard for the box costs 0.1c/cm, but the cardboard for the bottom is thicker, so it costs three times as much. Find the dimensions that will minimize the cost of the cardboard, to the nearest tenth of a centimeter.3. A piece of sheet metal, 60cm by 30cm, has a square cut out of each corner, and then the sides are folded up to make a rectangular box with an open top. Determine the dimensions that will maximize the volume of the box, to the nearest tenth of o centimeter. A cylindrical-shaped Tin can musT have a capaciTy of 1000 cm3. a) DeTer'mine The dimensions ThaT require The minimum amounT of Tin for The can, To The nearesT hundredTh of a cenTimeTer. According To The markeTing deparTmenT, The smallesT can ThaT The markeT will accepT has a diameTer of 6cm and a heighT of 4cm. b) WhaT is The raTio of The heighT To The diameTer