DIRECTIONS: Answer the following problems. NO SOLUTION NO SCORE. 1-2) Find the equation of the tangent and normal line to y = 2xv3x - 1 at x = 2. 3) Find the points of the graph y = 2x3 + 3x2 - 12x + 1 where the tangent is horizontal. 4) Find all the critical points of the function y = x3 - 6x2 +9x -3 5) Find the absolute extrema of y = x3 - 12x + 23 on the interval [-5, 3]. 6-7) Work-out a Calculus-based analysis of properties then sketch the graph of f(x) =2x2 -7x - 15 8-9) A rectangular box is to be made from a piece of cardboard 12 in long and 5 in wide by cutting out identical squares from the four corners and turning up the sides. Find the volume of the largest rectangular box that can be formed. 10) A ladder 7 meters long is leaning against a wall. If the bottom of the ladder is being pushed horizontally towards the wall at 3 m/s, how fast is the top of the ladder moving when the bottom is 5 meters from the wall